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Question: <p>Is there a list of basic quantum variables/attributes that all quantum particles have? </p>
<p>Ex. An electron has charge, position, speed, momentum, etc. Is there a complete list of these variables? </p>
<p>I would figure not all quantum particles share the same set of variables? A photon has position a... | https://physics.stackexchange.com/questions/66592/list-of-the-basic-quantum-mechanical-variables |
Question: <p>I am studing the Grover operator. Let be $x_0$ the marked element. Let be $t_f = \pi/2\omega$. The measurement of the register in the computational basis return $x_0$ with probability </p>
<p>$$p_{x_0}(t_f)=\langle x_0|U^{t_f}|D\rangle|=1-1/N$$</p>
<p>Where $|D\rangle$ is a diagonal state state, $U$ the ... | https://physics.stackexchange.com/questions/66813/spectral-decomposition-grover-operator |
Question: <p>First of all, this question is going to seem a a bit of philosophy but know that vague and purposeless wandering is certainly not what i'm trying to propose here.<br>
Also, the reason i didn't post in philosophy communities is that they certainly know a lot less ( if anything ) of quantum mechanics than mo... | https://physics.stackexchange.com/questions/68498/consequences-of-quantum-mechanics |
Question: <p>To construct a N-body anti-symmetric wave function some derivations start with the requirement that the N-body wave function should be anti-symmetric under a permutation of coordinates, other derivations start with the requirement that the total wave function should be anti-symmetric under a permutation of... | https://physics.stackexchange.com/questions/68673/is-a-permutation-of-coordinates-or-labels-really-equivalent |
Question: <p>I know that electron has mass , and that is particle( a body which has only mass and whose size is negligible) but can we ever calculate the volume of the electron . if yes how much it is . if no why?</p>
Answer: | https://physics.stackexchange.com/questions/68717/what-is-the-volume-of-electron |
Question: <p>Consider the particle in a box problem in QM. The crux of the reason why QM is able to explain the physical phenomenon is not just the theory but also able to impose boundary conditions which eventually result in quantization. Now in the particle in a 1-d box problem, the wave function is assumed to be zer... | https://physics.stackexchange.com/questions/70410/quantization-for-particle-in-a-box-problem |
Question: <p>I am still working on the Feynman path integral, more specifically on the case of a free particle with an infinite potential wall, i.e. the quantum system defined by the Hamiltonian </p>
<p>$$H_1 = \frac{\mathbf{P}^2}{2m} + V(\mathbf{Q})$$</p>
<p>where $V(\mathbf{Q})$ is the potential defined by</p>
<p>... | https://physics.stackexchange.com/questions/71667/potentials-in-feynman-path-integral-ii |
Question: <p>You have a photon traveling with E=hf and you trap it between two perfectly reflecting mirrors (like a QM particle in a box). The photon has to make a standing wave between the mirrors and its spacial frequency is dependant on the distance between the mirrors, L. Its time frequency, and hence energy are de... | https://physics.stackexchange.com/questions/71840/where-does-the-change-in-energy-come-from-when-trapping-a-photon-between-mirrors |
Question: <p>How do we calculate the expectation value for speed? I have heard that we must first calculate the expectaion value for kinetic energy. Someone please explain a bit what options do we have.</p>
Answer: <p>Calculating the energy eigenvalue, will give you $\langle v^2 \rangle$. This is how it's done:</p>
<... | https://physics.stackexchange.com/questions/73445/qm-calculating-expectation-value-for-velocity-of-an-electron |
Question: <p>Suppose we have an orthonormal basis $\{ \psi \}$ in finite dimension of a hilbert space;
What is the butterfly operator of a sum of the $ \psi $, say $\psi_i +\psi_j$ ?</p>
<p>Since by linearity of "taking the dual" we must have, writing $B$ for but..terfly,
$\lvert\psi_i +\psi_j\rangle\langle\psi_i +\p... | https://physics.stackexchange.com/questions/74995/what-is-a-ket-of-a-vector-with-a-bra-of-another-one |
Question: <p>For projector $p$, in finite dimension say, some unitaries $u, v$ does $upu^\dagger = vpv^\dagger$ implies $u = v$ ?
Intuitively, can we not say that a unitary is matrix permuting the basis and since $p$ is diagonal then obviously $u$ is $v$ ?
But for an exact proof ?</p>
<p>what if further, $p = upu^\dag... | https://physics.stackexchange.com/questions/75282/a-projector-equal-to-its-own-conjugate-by-a-unitary |
Question: <p>Looking at the <a href="http://en.wikipedia.org/wiki/Nakajima-Zwanzig_equation" rel="nofollow">Nakajima-Zwanzig equation</a>, wich gives the time evolution of a projection $\cal {P} \rho$ of a full density matrix $\rho$, I am wondering if the trace of $\cal P \rho$ is preserved under time evolution.</p>... | https://physics.stackexchange.com/questions/77869/does-the-nakajima-zwanzig-equation-preserve-the-trace-of-the-projected-density-m |
Question: <p>I came across this proportionality statement in my quantum mechanics notebook:
$\psi(x,t)$ is proportional to </p>
<p>$$
\begin{align}
\cos(kx - wt) &= \exp(i(kx-wt)) + \exp(-i(kx-wt)) \\
&= \exp (i(kx-wt))
\end{align}
$$
I looked through most commonly used textbooks for quantum mechanics and I c... | https://physics.stackexchange.com/questions/79058/probability-amplitude-in-basic-quantum-mechanics |
Question: <p>Consider an observable that can be described by a hermitian operator $A$ . No explicit relationship with time is given. What would happen to the probability if the quantity is measured a few days later? </p>
Answer: <p>The time evolution of observables in the Schrodinger picture is determined by the wave ... | https://physics.stackexchange.com/questions/81773/hermitian-operators-in-time-and-measurements |
Question: <p>On my midterm today, I read that when the deBroglie wavelength of a particle exceeds the spacing between the particles in a solid or liquid, the particles begin to behave quantum dynamically. Why is this? I thought a larger deBroglie wavelength implied a less quantum mechanical behavior.</p>
Answer: <p>Th... | https://physics.stackexchange.com/questions/81872/quantum-regime-of-particles-in-solids |
Question: <p>I need the derivation of Bethe formula for stopping power, but I can't see the corresponding paper to this matter.</p>
<blockquote>
<p>Application of Ordinary Space-Time Concepts in Collision Problems and Relation of Classical Theory to Born's Approximation. E. J. Williams. <a href="http://dx.doi.org/10... | https://physics.stackexchange.com/questions/80525/how-to-derive-the-bethe-stopping-power-formula |
Question: <p>Considering the free evolution of a Gaussian wave packet, is it possible to use Ehrenfest's theorem to determine the average value of momentum given that of position? </p>
<p>And I imply the simplified version of the theorem, namely $\frac{\mathrm d}{\mathrm d t}\langle x \rangle = \frac{1}{m}\langle p \r... | https://physics.stackexchange.com/questions/82002/ehrenfests-theorem-on-gaussians |
Question: <p>How many quantum numbers are needed to describe a stationary state of a particle in a multi-dimensional quantum box (say 73)?</p>
Answer: <p>Generalizing from 1d. For every of the $d$ dimensions you have one independent momentum variable $k_i$ such that $i\in\{1..d\}$. The boundary conditions quantize the... | https://physics.stackexchange.com/questions/86505/quantum-box-and-quantum-number |
Question: <p>Suppose you prepare a two-particle system such that $\Psi(\vec{r}_1,\vec{r}_2, t_0) = \Psi_1(\vec{r}_1, t_0)\Psi_2(\vec{r}_2, t_0)$.</p>
<p>So then, initially $\Psi(\vec{r}_1,\vec{r}_2,t_0) - \Psi_1(\vec{r}_1, t_0)\Psi_2(\vec{r}_2, t_0) = 0$</p>
<p>But now you let the system evolve in time and $\Psi(\vec... | https://physics.stackexchange.com/questions/87807/decomposition-of-two-particle-wavefunction-into-product-of-single-particle-wavef |
Question: <p>While introducing Clebsch-Gordan coefficients, they state that the operators:
$$ \vec{J_1}^2,\vec{J_2}^2,J_{1z},J_{2z}$$
form a complete set of compatible observables. Which means that there is no degeneracy in their common eigenspaces. </p>
<p>What I wonder is, how it follows that (if the above operators... | https://physics.stackexchange.com/questions/91071/total-angular-momentum-operator-forms-a-complete-set-clebsch-gordan-coefficien |
Question: <p>Does observation collapse the wave function, thus preventing an object from tunneling to a classically forbidden region?</p>
<p>If I understand correctly, observation causes objects to collapse into the state in which they were observed, so there will no longer be a probability of finding them elsewhere. ... | https://physics.stackexchange.com/questions/92520/does-measurement-prevent-tunneling |
Question: <p>I am reading a quantum transport book, where they often mention: phase breaking length and Fermi wavelength. I have looked up and found that:</p>
<p><strong>Phase breaking length</strong>= length over which electron remains its phase.</p>
<p><strong>Fermi wavelength</strong>= Wavelength associated with t... | https://physics.stackexchange.com/questions/93471/difference-fermi-wave-length-vs-phase-breaking-length |
Question: <p>Suppose you have a quantum system with a Hamiltonian having some number (greater than 2, possibly infinite) of eigenfunctions, and that the system is prepared in the ground state.</p>
<p>When can you approximate it as by two-level system (using just the ground state and first excited state)? Is there some... | https://physics.stackexchange.com/questions/93589/approximating-evolution-as-occurring-in-a-two-dimensional-subspace |
Question: <p>I have two quantum systems, a probe and a target that have been entangled. The probe is prepared in a mixed state and so has the target. Is the combined system therefore a mixed state?</p>
<p>If I had prepared my target in a pure state and probe in a mixed is the resulting combined system still a mixed st... | https://physics.stackexchange.com/questions/95793/when-combining-two-quantum-states-is-there-any-rules-that-say-its-going-to-be-in |
Question: <p>Let $b_k^\dagger ,b_k$ represent the creation and annihilation operators for an electron in state $k$. Let $d_j^\dagger ,d_j$ represent the same for a positron in state $j$. And let
$|0\rangle$ represent the vacuum.</p>
<p>Is it possible to have a state described by $ \left( b_k^\dagger + re^{i\theta} ... | https://physics.stackexchange.com/questions/31793/superposition-of-electron-and-positron-particle-states |
Question: <p>I am working on a concept for something and i want to make sure i understand something clearly before i start on everything else. Note, my project is more about the interactions of elements of complex systems rather than physics. Im just using this paragraph as an example, not doing a project on quantum ... | https://physics.stackexchange.com/questions/34035/is-this-paragraph-on-probabilities-of-sub-atomic-partials-accurate |
Question: <p>For linear momentum I can use the de Broglie equation, but what about energy in terms of moment of inertia or some other form? </p>
Answer: | https://physics.stackexchange.com/questions/35773/beginning-with-an-arbitrary-classical-equation-for-energy-how-do-i-get-the-qm-h |
Question: <p>As the title says, does a particle lose its location wavefunction if its location is measured exactly (I know this would be impossible in reality)?</p>
<p>Also, in reality, if one measures a particle, does the wavefunction of a particle become something different from original afterwards?</p>
Answer: <p>... | https://physics.stackexchange.com/questions/35827/does-a-particle-lose-its-location-wavefunction-if-its-location-is-measured-exa |
Question: <p>I recall vaguely that energy is absorbed/radiated in packets called quanta. Quanta were what are now known as photons. </p>
<p>What I'm curious about - Is absorption/radiation vis-a-vis photon lossy? Do the total number of photons exactly match the energy acquired/released?</p>
Answer: <p>It is not a los... | https://physics.stackexchange.com/questions/35343/is-emission-absorption-of-a-photon-lossy |
Question: <p>How can energy be quantized if we can have energy be measured like in 1.56364, 5.7535, 6423.654 kilo joules, with decimals? Thanks</p>
<p>Also isnt it quantization means energy is represented in bit quantities meaning you can not divide, lets say 1 bit of energy</p>
Answer: <p>Typically, in quantum mecha... | https://physics.stackexchange.com/questions/38433/energy-is-quantized |
Question: <p>I've just started on QM and I'm puzzled with a lot of new ideas in it.</p>
<p>1.On a recent lecture I've attended, there is an equation says:
$\langle q'|\sum q|q\rangle \langle q|q' \rangle =\sum q \delta(q,q')$</p>
<p>I don't understand why $\langle q'|q\rangle \langle q|q' \rangle =\delta (q,q')$</p>
... | https://physics.stackexchange.com/questions/39540/something-i-dont-understand-in-quantum-mechanics |
Question: <p>My understanding of quantum mechanics is that the state of a system is represented by a vector in multidimensional complex vector space. Is there, in principal, a state vector that represents a large, classical object such as, say, a cheeseburger, at an instant in time? If so, what is the physical meaning ... | https://physics.stackexchange.com/questions/41740/is-there-a-quantum-state-for-a-large-system |
Question: <p>Prove that
$$ \lambda _{1}\lambda _{2}^{*}\varphi _{1}\varphi _{2}^{*}+\lambda _{1}^{*}\lambda _{2}\varphi _{1}^{*}\varphi _{2}
\leq \left | \lambda _{1} \right |\left | \lambda _{2} \right |\left \{ \left | \varphi _{1} \right |^{2}+\left | \varphi _{2} \right |^{2} \right \} $$
where all symbols are co... | https://physics.stackexchange.com/questions/44218/how-can-i-prove-this-inequality |
Question: <p>Can someone explain to me the origin of the exchange interaction between two electrically charged spin 1/2 fermions? Quantitative or qualitative accepted. </p>
Answer: <p>The wave function is antisymmetric under exchange of (all) the coordinates of each electron (we'll just call them electrons since that'... | https://physics.stackexchange.com/questions/46185/origin-of-exchage-interactions |
Question: <p>How to take differential of Quantum mean value over hermitian operator (mean or expectation value)?
$$d\langle \hat A\rangle$$
remark:
or time evolution of mean value over operator
$$\frac {d\langle \hat A\rangle}{dt}$$</p>
<blockquote>
<p>what is the problem here?
ok let me talk a little more special... | https://physics.stackexchange.com/questions/46722/differential-of-quantum-mean-value-or-expectation-value |
Question: <p>I don't understand the superposition principle in quantum mechanics or the collapse of wave-function (I think it's impossible for me to understand it) My question is: </p>
<p>Is it possible to demonstrate the quantum mechanical behaviour (Superposition and wavefunction collapse, etc.) in some macroscopic ... | https://physics.stackexchange.com/questions/51570/quantum-mechanics-in-macroscopic-systems |
Question: <p>There is a thread in Physicsforums.com which states due to Quantum Mechanics, if you wait long enough diamonds will appear in your pocket, it also states it's possible for all your atoms to spontaneously re-arrange themselves so you turn into a Boeing airplane. Surely this is fiction?</p>
Answer: <blockqu... | https://physics.stackexchange.com/questions/51627/quantum-mechanics-whats-possible |
Question: <blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="https://physics.stackexchange.com/questions/48469/intuitive-meaning-of-hilbert-space-formalism">Intuitive meaning of Hilbert Space formalism</a> </p>
</blockquote>
<p>I am totally confused about the Hilbert Space formalism of Quantum Me... | https://physics.stackexchange.com/questions/52252/intuitive-meaning-of-the-hilbert-space-formalism |
Question: <p>Quantum mechanics says that atoms are invisible - they do not have some specified location, only a probability distribution. So, how can we see them? If there is to be particle-antiparticle annihilation (or other interactions), the particles must have a fixed location, right? So, is this process just rando... | https://physics.stackexchange.com/questions/53422/how-do-particles-such-as-electrons-become-visible |
Question: <p>The quantum state of a system is supposed to contain all the information that can be obtained about the system such as its energy, momentum...etc.</p>
<p>So I have 2 questions:</p>
<p>1-If someone gave us a quantum state of a single particle, can we tell of what mass it is?</p>
<p>2-Another question is ... | https://physics.stackexchange.com/questions/53429/given-a-state-function-of-a-particle-can-we-determine-its-mass |
Question: <p>Since the energy levels of atoms are quantized, I was wondering what happens if an electron is hit by a photon whose energy is higher than electron's first excited state but lower than second excited state. Does it excite to the first excited state? If yes, what happens to the remaining energy?</p>
Answer... | https://physics.stackexchange.com/questions/53790/what-happens-if-an-atom-absorbs-a-photon-of-energy-higher-than-first-excited-sta |
Question: <p>In this experiment we only consider the force at z direction, but $\vec B$ field gradient doesn't exclusively exist at z direction according to Maxwell's equations. So why don't we see the splitting in other directions?</p>
Answer: <p>The point made by Otto Stern in the <a href="http://positron.physik.un... | https://physics.stackexchange.com/questions/59491/force-analysis-of-silver-atom-in-stern-gerlach-experiment |
Question: <p>If you have two particles of the same species , Quantum mechanics says that $\Phi_{m_{1},x_{1},p_{1},m_{2},x_{2},p_{2}}=\alpha\Phi_{m_{2},x_{2},p_{2},m_{1},x_{1},p_{1}}$
But I don't understand why $\alpha$ doesn't depend on $x$ , $p$ . If $\alpha$ depends on $SO(3)$ invariants as $x^2 , x.p , p^2$ etc th... | https://physics.stackexchange.com/questions/59570/indistinguishable-particles-in-quantum-mechanics |
Question: <p>In my reading of blackbody radiation I am always asked to imagine this or that body being a perfect absorber or emitter of radiation, and I am always left with the impression that a blackbody exists only as a theoretical construct. But is it? Or can one be constructed and tested? </p>
Answer: <p>A <a href... | https://physics.stackexchange.com/questions/59894/is-a-blackbody-real-or-imagined |
Question: <h2>Question Statement</h2>
<blockquote>
<p>Consider a proton which has spin $1/2$ that is free to move throughout all locations $-\infty<x<\infty$. A magnetic field of constant magnitude $B_{\circ}$ is applied perpendicular to the $x$ axis. Let the Hamiltonian be given by:
$$
\mathcal{H}=\frac{\ha... | https://physics.stackexchange.com/questions/62061/free-1d-proton-in-magnetic-field |
Question: <p>Why is it assumed that in this experiment, the jump will be between the second and the first states. Couldn't it be that when the electrons have enough energy, an atom absorbs enough to get to the third state and then jumping only to the second, emiting less energetic light?</p>
<p>Isn't this right? Or is... | https://physics.stackexchange.com/questions/65514/frank-hertz-experiment-and-different-jumps |
Question: <p>I know that an inner product between two vectors is defined like: </p>
<p>$$\langle a | b\rangle = {a_1}^\dagger b_1+{a_2}^\dagger b_2+\dots$$</p>
<p>but because a transpose of a component for example $a_1$ is again only $a_1$ the above simplifies to: </p>
<p>$$\langle a | b\rangle = \overline{a_1} b_1+... | https://physics.stackexchange.com/questions/65779/expectation-value-zetilli-vs-griffith |
Question: <p>In <a href="http://www.goodreads.com/book/show/8514649-quantum-mechanics" rel="nofollow">Zetilli's</a> book author says that we can interpret an inner product $\langle x | \psi(t) \rangle$ as a wave function $\psi (x,t)$ and i understand this.</p>
<p>Next he talks about how a state of the system $|\psi(t)... | https://physics.stackexchange.com/questions/66096/qm-the-superposition-principle |
Question: <p>Given a Hilbert space of finite dimension $N$ with an orthonormal basis $\mathcal{B}=\{|0\rangle,\ldots,|N-1\rangle \}$ what is the most general unitary operation that commutes with the projector onto one of the basis elements (say $|0\rangle$), \emph{i.e.}, what is the most general $\mathcal{U}$ such that... | https://physics.stackexchange.com/questions/66097/what-is-the-most-general-unitary-that-commutes-with-a-one-dimensional-projector |
Question: <p>I'm contemplating particle-hole symmetry, and as an example I am looking at either an electron moving along a hypothetical lattice of hydrogen ions, or a hole moving along a hypothetical lattice of helium atoms. </p>
<p>According to some lecture notes I found, the hopping integral I get when I treat this ... | https://physics.stackexchange.com/questions/5083/electron-hole-symmetry-in-h-and-he |
Question: <p>The Schrodinger equation governs the possible time evolution of a wave function, expressed as a partial differential equation. Isn't this equivalent to the simpler equation</p>
<p>$$\omega = \hbar k^2/2m$$</p>
<p>i.e. any wave function that satisfies this dispersion relation will also satisfy Schrodinge... | https://physics.stackexchange.com/questions/5224/why-is-it-necessary-to-represent-schrodingers-equation-as-a-partial-differentia |
Question: <p>This should be a very easy question. If you look at the bottom of "Identical Particles" in Wikipedia, you see Table 1, which gives you the two particle statistics for bosons, fermions and distinguishable particles. The problem is to extend this table for three, four and five particles, or give an equival... | https://physics.stackexchange.com/questions/7245/what-are-the-statistics-of-three-to-five-bosons |
Question: <p>Inspired by this: <a href="https://physics.stackexchange.com/questions/8937/electrical-neutrality-of-atoms">Electrical neutrality of atoms</a></p>
<p>If I have a wavefunction of the 'reduced mass coordinate' for a hydrogen like atom made from an electron and a positron, what is the spatial charge distribu... | https://physics.stackexchange.com/questions/8944/charge-distribution-in-positronium |
Question: <p>So I am looking through my book and it says ".... the order of the excited states is exactly the same order (3p-4s-3d-4p)".</p>
<p>But now I am looking at a question in the book and it says "Is 3d to 4s transition possible? Why or why not?"</p>
<p>My answer to this question is: No it can't be because it ... | https://physics.stackexchange.com/questions/8991/quick-question-on-the-ionization-energy-and-the-selection-rule |
Question: <p>I don't know about all the details of Bell tests using methods like parametric down conversion, but at least in some versions of the EPR paradox you get two photons moving apart in opposite directions. I wonder if you can look for detection coincidences by using photographic plates instead of coincidence c... | https://physics.stackexchange.com/questions/9170/bell-tests-using-position-measurement |
Question: <p>I am trying to "decode"/derive an expression for the macroscopic rate constant for the tunneling of protons through a potential energy barrier that I read in a journal article:
$$
k_{\rm tun}(T)=(2\pi\hbar)^{-1}\int_0^{V_{\rm max}} Q(V,T) P_{\rm tun}(V)\ dV.
$$
So basically: the authors say work out the ... | https://physics.stackexchange.com/questions/9506/tunneling-rate-constant |
Question: <p>Spin echo experiments have been able to reverse the motions of all the molecules in a gas in statistical mechanics in the manner of Loschmidt. The Fermi-Ulam-Pasta model has solutions with a single mode dispersing, only to recohere after quite some time has elapsed. Can the same thing happen for decoherenc... | https://physics.stackexchange.com/questions/10201/what-are-the-conditions-for-decoherence-to-be-irreversible |
Question: <p>In the following excerpt from S. Gasiorowicz's <em>Quantum Physics</em>, he derives an expression for the average momentum of a free particle. $\psi(x,t)$ is the wave function of a free particle, $\psi^*$ denotes its complex conjugate.</p>
<blockquote>
<p>We try the following: since classically,</p>
... | https://physics.stackexchange.com/questions/9705/why-is-fracdxdt-0-in-this-average-momentum-calculation |
Question: <p>A book by C. J. Ballhausen led me to believe that a quick way to check that I performed step operators properly was by observing that the "wave function should appear normalized," but I have found some issue applying this in practice and believe it is due to my misunderstanding of the underlying physics; I... | https://physics.stackexchange.com/questions/11740/wave-function-normalization |
Question: <p>Can Heisenberg's Uncertainty principle be rewritten in terms of energy density</p>
<p>writing
$$\Delta E \Delta T \geqslant \hbar/2$$
in factors of energy density
$\Delta \sigma \text{ }= \frac{3\Delta E}{4\pi r^3}$</p>
<p>I get
$$\Delta \sigma \frac{3\text{$\Delta $T}}{4\pi r^3} \geqslant \hbar/... | https://physics.stackexchange.com/questions/12636/heisenbergs-uncertainty-forms |
Question: <p>What is the basic postulate on which QM rests. Is it that the position of a particle can only be described only in the probabilistic sense given by the state function $\psi(r)$ ? We can even go ahead and abandon the particle formalism as well. So what is the QM all about ? A probabilistic description of th... | https://physics.stackexchange.com/questions/13639/what-is-the-basic-postulate-on-which-qm-rests |
Question: <p>The weight function comes from Dirac's book, PRINCIPLES OF QUANTUM MECHANICS. On page 66,he says that sometimes it is more convenient not to normalise the eigenvectors, i.e. $$\langle\xi_1'...\xi_u'|\xi_1''...\xi_u''\rangle=\rho'^{-1}\delta(\xi_1'-\xi_1'')...\delta(\... | https://physics.stackexchange.com/questions/15051/weight-function-and-the-metric |
Question: <p>I'm a math student who's dabbled a little in physics, and one thing I'm a little confused by is separation of variables. Specifically, consider the following simple example: I have a Hamiltonian $H$ which can be written as $H_x + H_y + H_z$ depending only on $x,y$, and $z$ , respectively, and I want to fin... | https://physics.stackexchange.com/questions/15949/separation-of-variables |
Question: <p>let be a Hamiltonian in one dimension, i would like to evaluate the functional determinant $ det(E-H) $ in onde dimension</p>
<p>i believe that $ det(E-H)= Cexp(iN(E)) $ here $ N(E)$ is the number of energy levels less than a given number 'E'</p>
<p>my steps</p>
<ol>
<li><p>i use the identity $ logDet(... | https://physics.stackexchange.com/questions/16477/functional-determinant-and-wkb-approximation |
Question: <p>In the literature, sometimes one reads that decoherence is due to the coupling of the system to the external environment, and sometimes one reads that it is due to coarse graining over the microscopic degrees of freedom. Are these two different cases of decoherence, or is one more fundamental than the othe... | https://physics.stackexchange.com/questions/16297/is-decoherence-due-to-coarse-graining-or-coupling-with-the-environment |
Question: <p>Frequentism is the philosophy that probabilities are statistical in the sense that they give the limiting frequency ratios of outcomes as the number of trials is large enough. For tiny probabilities like exponentially small probabilities, would this require exponentially many trials?</p>
<p>I know, I know... | https://physics.stackexchange.com/questions/17189/does-frequentism-require-exponentially-many-trials-in-some-cases |
Question: <p>In some literature there is reference to $\tau$ matrices which are the same pauli matrices in an orthogonal space. I have not seen any explicit constructions of this anywhere. Could someone tell me or point to literature on how to find the matrix elements of these $\tau$ matrices. </p>
Answer: <p>Georgi i... | https://physics.stackexchange.com/questions/18018/pauli-matrices-in-orthogonal-space |
Question: <p>I'll apologize in advance if this is not an appropriate place for my question. My background is not in physics, and my understanding of quantum mechanics is extremely rudimentary at best, so I hope you'll be forgiving of my newbish question.</p>
<p>Given a system of entangled particles (eg, 2 or more ele... | https://physics.stackexchange.com/questions/19464/does-an-interaction-of-entangled-particles-with-each-other-cause-decoherence |
Question: <p>Let me clarify this question somewhat. I know decoherence is ubiquitous in nature and explains the emergence of a classical world from quantum physics. My question is really about how a knowledge of how decoherence actually works can be put to use in a practical application. An application we can't design ... | https://physics.stackexchange.com/questions/20400/what-are-the-practical-applications-of-decoherence |
Question: <p>Given a stationary 1-D wave function $\psi(x)$, how is the derivative in the momentum operator interpreted?</p>
<p>$$
\int_{-\infty}^\infty \psi^*(x) \hat{p} \psi(x) dx
= \int_{-\infty}^\infty \psi^*(x) (-i\hbar\nabla) \psi(x) dx
$$</p>
<p>Should the integral be interpreted as</p>
<p>$$-i\hbar\int_{-... | https://physics.stackexchange.com/questions/23036/how-to-interpret-the-derivative-in-the-momentum-operator-in-quantum-mechanics |
Question: <p>An electron is orbiting two protons. With the Born-Oppenheimer approximation that the protons do not move, I'd write the Hamiltonian of the electron's movement as:</p>
<p>$$ \mathbf{H} = -\frac{\hbar^2}{2m}\nabla^2 + E_p$$</p>
<p>with</p>
<p>$$E_p = -\frac{e^2}{4\pi \epsilon_0}\left(\frac{1}{r_1}+\frac{... | https://physics.stackexchange.com/questions/23569/in-h-2-what-is-the-hamiltonian-of-the-movement-of-the-electron |
Question: <p>I have heard couple of times about the concept of wave function of the universe, an object that would capture every degrees of freedom inside it (every particle, me, even you dear reader, etc...) and it always sounded fallacious or at least non pertinent, what would be the point of using that gigantic obje... | https://physics.stackexchange.com/questions/24032/pertinence-of-the-wave-function-of-the-universe-or-complete-description-of-syst |
Question: <p>what is difference between these two expectation values $\langle \hat A \hat B\rangle$ and $\langle \hat B \hat A\rangle$?
where the $\hat B$ and $\hat A$ are two operators.</p>
Answer: <p>$$\langle \hat{A}\hat{B} \rangle -\langle \hat{B}\hat{A} \rangle = \langle \hat{A}\hat{B}-\hat{B}\hat{A} \rangle$$</p... | https://physics.stackexchange.com/questions/30155/what-is-difference-between-these-two-expectation-values |
Question: <p>I have been told that Feynman deduced from a path integral formulation an equation that predicts the amount of time it would take for a diamond to 'jump' out of a box:</p>
<p>$t > \dfrac{x \Delta{x} m}{ h} $</p>
<p>where $x$ is the size of the box, $\Delta x$ is the distance the diamond must travel to... | https://physics.stackexchange.com/questions/30172/feynmans-diamond-jumping-out-of-a-box-parody-how-would-this-work |
Question: <p>$\renewcommand{\ket}[1]{\left\lvert #1 \right \rangle}$</p>
<p>If a quantum system $A$ becomes entangled with another quantum system $B$, then $A$ can no longer be described by a pure quantum state.
For example, given a Bell state
$$
\ket{00} + \ket{11} \, ,
$$
the state of either qubit by itself is a... | https://physics.stackexchange.com/questions/409753/partial-decoherence-from-interaction-between-two-qubits |
Question: <p>Is there any difference when we say in quantum mechanics the <em>eigenfunction</em> of an operator and the <em>state function</em>? Can we use the two terms as supplementary to one another?</p>
Answer: | https://physics.stackexchange.com/questions/425519/difference-between-state-function-and-eigenfunction |
Question: <p>If I glow a white LED bulb and then put a color filter around it (for example, a red color filter or a violet color filter) , then will it change the frequency of light.</p>
Answer: <p>The frequency will not be changed, but rather the color that is reflected/transmitted (depending on the nature of the fil... | https://physics.stackexchange.com/questions/426844/does-color-filter-change-the-frequency-of-light |
Question: <p>I know that electrons behaves as a particle instead of waves once observed under a light source.
But what I really want to know is that how the photon particles are forcing the electrons to deviate from their wave character?</p>
Answer: | https://physics.stackexchange.com/questions/430914/how-light-source-effects-the-nature-of-electron-in-double-slit-experiment |
Question: <p>In a recent <a href="https://www.nature.com/articles/s41467-018-05739-8.pdf" rel="nofollow noreferrer">paper</a>, “Quantum theory cannot consistently describe the use of itself”, D. Frauchiger and R. Renner describe a modified Schroedinger's Cat <em>gedankenexperiment</em>, in which there are two boxes (... | https://physics.stackexchange.com/questions/431053/error-in-paper-showing-internal-inconsistency-in-qm |
Question: <p>I'm watching <a href="https://www.youtube.com/watch?v=EftlcEdaO_8&list=PLy73XOgPrzuYW-RBSJz8IbdanXgIUuwsR&index=17" rel="nofollow noreferrer">Lecture 03-05 of the MIT 3.024 lecture series on Electronic, Optical and Magnetic Properties of Materials</a> by Polina Anikeeva, specifically the discussion... | https://physics.stackexchange.com/questions/433443/how-do-you-calculate-the-probabilities-associated-with-eigenfunctions-of-a-wave |
Question: <p>I'm studying distinguishability in quantum mechanics but I'm confused with the calculation of energies.</p>
<p>Suppose we are given a hamiltonian for 1 particle with two possible sites<br>
<span class="math-container">$$ H = \begin{bmatrix}
0 & t \\
t & 0
\end{bmatrix}$$</span></p>
<p>W... | https://physics.stackexchange.com/questions/440262/distinguishability-and-energy-of-a-system |
Question: <p>Imagine an electron in atomic or ascillator potential - any bound electron state. The WF has bell like shape fading at infinity - where classical energy of the electron by all means greatly exceeds the state energy eigenvalue. Now, if we place a trap for the electron at this distance and finally get the el... | https://physics.stackexchange.com/questions/441452/seeming-energy-paradox-in-quantum-system |
Question: <p>Picture a planet wandering intergalactic space. Such a planet would only couple to vacuum flucuations and the cosmic microwave background. (Ignore stray Hydrogen atoms.)</p>
<p>If this planet started as a pure quantum state, how fast would that state lose its coherence?</p>
<p>In such a system, clearly... | https://physics.stackexchange.com/questions/442432/planetary-sized-pure-quantum-states |
Question: <p>In Bose Einstein condensate photons stop moving, but with reference to what frame of reference? Photons move at constant speed in all reference frames so what happens to Maxwell equations at zero degree kelvin? </p>
Answer: <p>In a Bose-Einstein condensate the electrical field of the light interacts with ... | https://physics.stackexchange.com/questions/447059/bose-einstein-condensate |
Question: <p>in this <a href="https://arxiv.org/abs/quant-ph/9609002" rel="nofollow noreferrer">relational quantum mechanics paper</a> Rovelli tries to reconstruct the theory avoiding to use the notion of a state associated to a particle. he says that the only correct thing would be to speak
of the information tbat an ... | https://physics.stackexchange.com/questions/449641/how-can-we-use-usual-notations-in-relational-quantum-mechanics |
Question: <p>Can we proof the relation that the principal quantum number <span class="math-container">$n$</span> and azimuthal quantum number <span class="math-container">$l$</span> have the relation <span class="math-container">$l=0,1,...n-1$</span> in any spherical symmetric potential <span class="math-container">$... | https://physics.stackexchange.com/questions/450330/quantum-numbers-in-spherical-symmetric-potential |
Question: <p>Consider a two state system <span class="math-container">$\rho$</span> with some Hamiltonian <span class="math-container">$H$</span>. I am interested in the specifics of the systems time-evolution.</p>
<p>The article I am reading gives me the following time evolution:</p>
<p><span class="math-container"... | https://physics.stackexchange.com/questions/452481/deriving-time-dependent-hamiltonian |
Question: <blockquote>
<p><strong>When intuition fails: photons to the rescue!</strong><br>
When experiments were performed to look at the effect of light amplitude and frequency, the following results were observed:</p>
<ul>
<li>The kinetic energy of photoelectrons increases with light frequency.</li>
<li>Electric cur... | https://physics.stackexchange.com/questions/452798/photoelectric-effect-and-electric-current |
Question: <p>So, I have noticed something in the solutions of the infinite quantum well and I don't quite understand it. The solutions are of the form</p>
<p><span class="math-container">\begin{equation}
\phi_{n}(x) = A\cos(kx)+B\sin(kx)
\end{equation}</span></p>
<p>If the boundaries of the well are at <span class="m... | https://physics.stackexchange.com/questions/453228/why-the-available-parities-of-the-infinite-well-solutions-change-as-we-change-th |
Question: <p>The proof of the statement of Ehrenfest theorem in the Schrodinger picture does not depend on the state vector. However, <a href="https://en.wikipedia.org/wiki/Ehrenfest_theorem" rel="nofollow noreferrer">Wikipedia claims</a> that:</p>
<blockquote>
<p>for states that are highly localized in space, the e... | https://physics.stackexchange.com/questions/459903/ehrenfest-theorem-and-the-distinction-between-moment-ordinal-1-and-moment-ordina |
Question: <p>In introductory quantum mechanics books the topic of identical particles often introduces a "particle exchange" operator. This operator, when applied to a multi-particle wave-function, exchanges the positions of two identical particles.</p>
<p>However, it seems to me that this is a non-physical thing. P... | https://physics.stackexchange.com/questions/464019/does-the-particle-exchange-operator-have-any-validity |
Question: <p>In a double slit experiment,the fringes obtained on screen are due to superposition of single slit diffraction from each slit and the double slit interference pattern,</p>
<p>when we talk about single slit diffraction,we say the single slit is divided into many number of slits and the waves originating fr... | https://physics.stackexchange.com/questions/467873/which-waves-give-rise-to-interference-pattern-in-a-double-slit-diffraction-exper |
Question: <p>I was just wondering that as according to quantum mechanics electrons are present in many places at the same time, now as according to Einstein as <span class="math-container">$$E = mc^2$$</span> doesn't it violate energy conservation ?</p>
<p><code>Edit</code>-</p>
<p>I just meant by energy conservat... | https://physics.stackexchange.com/questions/469062/as-electrons-are-present-in-many-places-at-the-same-time-so-how-can-it-not-viola |
Question: <p>I have read that electrons fired individually through a 2 or more slits still form an interference pattern. I think this may be due to the fact that moving electrons produce electromagnetic waves (like in a transmitter aerial), and EM waves move electrons (like in your TV aerial). While each electron can o... | https://physics.stackexchange.com/questions/469718/electrons-fired-one-at-a-time-in-double-slit-experiment |
Question: <p>Does this question make sense? Can measuring the spin of one entangled particle 'determine' the polarization of the other?</p>
Answer: <p>When two particles become entangled, the whole new system will have a common wavefunction that will describe the whole system. This system in your case will have both ... | https://physics.stackexchange.com/questions/476238/can-different-types-of-properties-be-entangled-with-each-other-say-the-spin-of |
Question: <p>Consider electron spin operator. It acts on Hilbert space <span class="math-container">$\mathbb{C}^2$</span>. Next, electron position operator acts on space <span class="math-container">$\mathbb{L}^2$</span>. Can we describe all electron features in one, "joint" Hilbert space? Certainly, both spaces can be... | https://physics.stackexchange.com/questions/485410/not-separable-electron-state |
Question: <p>On pg 104 of "Introduction to Quantum Mechanics" by Griffiths, we are asked to find the eigenfunctions of the <span class="math-container">$x$</span> operator. Hence, we have to find functions such that <span class="math-container">$$x f(x)=\lambda f(x)$$</span> I have used the notation <span class="math-c... | https://physics.stackexchange.com/questions/485951/finding-the-eigenfunctions-of-the-operator-x |
Question: <p>We know a photon is absorbed when an electron's orbit expands, but what is the mechanism?</p>
<p>We know that an electron is not simply a particle, so the photon can't be converted into only kinetic energy.</p>
<p>Is the photon converted into space, thus increasing the orbital size?</p>
Answer: <p>The p... | https://physics.stackexchange.com/questions/489054/what-is-the-mechanism-when-a-photon-is-absorbed-causing-an-electron-orbital-expa |
Question: <p>Since the position of an electron is not determined, how is it’s mass distributed ? In other words, how does an electron curve space time ?</p>
<p>.</p>
Answer: | https://physics.stackexchange.com/questions/502287/how-is-the-mass-of-an-electron-distributed |
Question: <p>How can the results from <a href="https://www.nature.com/articles/s41567-019-0663-9.epdf?referrer_access_token=P6jczrHmpk_eNzSKdu3YCdRgN0jAjWel9jnR3ZoTv0MQ7n-_yUmyvBsKfkN6FLBu98G0Nrx30Fucun-h3w8WX9IlwWelmQLTVb70WHA4Y1pxsdPmhmq4QvZ3kk0dRycJILQYYHZN26qmO72UylFXKFgM9i70iUUDcZdPwblhMv0RzePEbjpRDvq9ofxAtGf2St2M... | https://physics.stackexchange.com/questions/507168/understanding-quantum-superposition-of-molecules |
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