conversations listlengths 2 2 |
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[
{
"from": "human",
"value": "Suppose I have two free-particles $A,B$ whose positions evolve according to wave functions $\\psi_A(x,t)$ and $\\psi_B(x,t)$. I am interested in talking about the position vector from $A, B$, and ideally I would like to describe it according to a wave function lets call it $\\ps... |
[
{
"from": "human",
"value": "PROBLEM 1.22 Give the hybridization state of each carbon in the following compounds:\n(f) Acrylonitrile (CH2=CHC≡N). What is the hybridization state of carbon in acrylonitrile (CH2=CHC≡N)?"
},
{
"from": "gpt",
"value": "Let's analyze the hybridization state of each c... |
[
{
"from": "human",
"value": "$V(p) $ is the Coulomb potential. I think this theory should be fine because Hamilton's equations are somewhat symmetric in $x$ and $p$. The momentum space Schrodinger equation will be:\n$$i\\frac{d\\psi }{dt}=V(p) \\psi +\\frac{d^2}{dp^2}\\psi$$\nwhich is pretty much the same a... |
[
{
"from": "human",
"value": "Let's consider free Maxwell theory:\n$$\nS_{Maxwell} = \\int d^dx \\; -\\frac{1}{4e^2}F_{\\mu\\nu}F^{\\mu\\nu}\n$$\nIn such theory one can define monopole operator using path integral via correlation functions with other operators:\n$$\n\\langle\\mathcal{M}(x) \\mathcal{O}_1(x_1... |
[
{
"from": "human",
"value": "The electronic wave function of a molecule is an antisymmetric product of 1-electron molecular spin-orbitals. Using the electronic wave function of \\( \\text{H}_2 \\) molecule derive the expression for the ground state electronic energy of the molecule in terms of 1- and 2-elec... |
[
{
"from": "human",
"value": "In trying to better understand the chiral-anomaly WZW-term interaction of the heavy vector mesons, I have trouble finding much relevant literature, but maybe I am looking in the wrong place. \nOne useful article I found is this one:\n\nS. Ozaki, H. Nagahiro, A. Hosaka, \n\"Magne... |
[
{
"from": "human",
"value": "Alkylating butanone with methyl iodide leads to two different products since there are a-protons on either side of the carbonyl group. One of these products is obtained specifically by using a β-keto ester to make the target alkylation site more acidic. What complication arises ... |
[
{
"from": "human",
"value": "I'm trying to prove that the QED Lagrangian\n$$\\mathscr{L}=\\bar{\\psi}(i\\!\\!\\not{\\!\\partial}-m)\\psi - \\frac{1}{4}F^{\\mu\\nu}F_{\\mu\\nu} - J^\\mu A_\\mu$$\nIs invariant under P and C. The two fields transform as\n$$A^\\mu(x) \\xrightarrow{P} - \\eta^*\\mathscr{P}^\\mu{... |
[
{
"from": "human",
"value": "Consider the probability of finding an electron within a region:\n$$P= \\iiint |\\psi(x,y,z)|^2 dxdydz$$\nI would think that The probability of finding an electron at a single point in space would be defined as:\n$$P(x,y,z)= \\lim_{dx,dy,dz\\rightarrow 0} \\int_{x}^{x+dx}\\int_... |
[
{
"from": "human",
"value": "The yellow crystalline antibiotic frustulosin was isolated from a fungus in 1978 and it was suggested the structure was an equilibrium mixture of **A** and **B**. Apart from the difficulty that the NMR spectrum clearly shows one compound and not an equilibrium mixture of two com... |
[
{
"from": "human",
"value": "The formation of allantoine from uric acid is evidence that the latter contains two urea residues, and the formation of alloxan that it contains the arrangement of atoms represented by the symbols, - \nN-C \nCC \nN-C \nThese facts lead to the view that the structure of uric ... |
[
{
"from": "human",
"value": "Initially, the alkyne is converted into the E-alkene via the intermediate linear cation. The activation energy for this step is labelled AG₁. The E-alkene can convert to the Z isomer via an intermediate, with activation energy AG2. Since AG₁ is smaller than AG₂, the E-alkene for... |
[
{
"from": "human",
"value": "I am currently taking thermodynamics and am finding the concept of thermodynamic equilibrium rather difficult to grasp. My textbook gives a definition in terms of the virtual displacement of with respect to virtual displacements of variable $x_1,x_2,\\dots,x_n$ and writes\n$$\\d... |
[
{
"from": "human",
"value": "Detailed features of the active site of RNA polymerase have been probed using modified RNA nucleotides that can react with nearby targets. In one study an analog of U carrying a reactive chemical group was incorporated at one of two positions in a radiolabeled RNA and then 'walk... |
[
{
"from": "human",
"value": "What do you mean by D- and L-descriptors of α-amino acids? Give examples. Are they related in any way with the CIP system of naming enantiomers containing chiral centres?"
},
{
"from": "gpt",
"value": "### D- and L-Descriptors of α-Amino Acids\n\nThe **D- and L-** sy... |
[
{
"from": "human",
"value": "Answer the Following:\\n\\n(a) (CH3)3N: is a stronger nucleophile than (CF3)3N. Comment on their basicities.\\n\\n(b) The order of reactivity of I- > Br- > Cl- > F- towards CH3Br in water is reversed in DMF solution. Explain.\\n\\n(c) Explain the effect of increase in solvent po... |
[
{
"from": "human",
"value": "(b). H2C=CH-CH2-Br →[Mg] H2C=CH-CH2-MgBr + H2C=CH-CH2-Br →[SN2] Molecular Formula: C10H16"
},
{
"from": "gpt",
"value": "Let's analyze the problem carefully step-by-step.\n\n---\n\n### Given:\n\n- Substrate: **H2C=CH-CH2-Br** (allyl bromide, also called 3-bromopropen... |
[
{
"from": "human",
"value": "Calculate the time required to deposit 7.00 g of silver from a solution of AgNO\\(_3\\) with a current of 4.00 A."
},
{
"from": "gpt",
"value": "**Given:**\n\n- Mass of silver to be deposited, \\( m = 7.00 \\, \\mathrm{g} \\)\n- Current, \\( I = 4.00 \\, \\mathrm{A} ... |
[
{
"from": "human",
"value": "I've been studying the interference phenomena observed in the double-slit experiment and came across a concept that piqued my interest. It is well understood that for interference patterns to form, the overlapping waves (or photons) must exhibit a degree of coherence. However, t... |
[
{
"from": "human",
"value": "The usual explanation goes as follows. Charge flows until the applied electric field is canceled by the induced field, giving a total field $\\vec{E} = \\vec{0}$. This is reasonable if one gives as an example a rectangular slab of conductor with a constant applied field $\\vec{E... |
[
{
"from": "human",
"value": "The industrial production of NH\\(_3\\) by use of a natural gas feedstock can be represented by the following simplified set of reactions:\\n\\n1. \\( \\text{CH}_4 + \\text{H}_2\\text{O} \\rightarrow \\text{CO} + 3\\text{H}_2 \\) \\n2. \\( 2\\text{CH}_4 + \\text{O}_2 \\rightarr... |
[
{
"from": "human",
"value": "Find an equation of the normal plane to the curve that is the intersection of 9x^2 + 4y^2 - 36z = 0 and 3x + y + z - z^2 = 1 at the point (2, -3, 2)."
},
{
"from": "gpt",
"value": "Given the curve as the intersection of two surfaces:\n\\[\n\\begin{cases}\n9x^2 + 4y^2... |
[
{
"from": "human",
"value": "The reaction \\(2\\text{HI} \\rightleftharpoons \\text{H}_2 + \\text{I}_2\\), at equilibrium contained 7.8 g, 203.2 g and 1638.4 g of \\(\\text{H}_2\\), \\(\\text{I}_2\\) and \\(\\text{HI}\\), respectively. Calculate \\(K_c\\)."
},
{
"from": "gpt",
"value": "Given th... |
[
{
"from": "human",
"value": "How does one calculate the available energy in the transitions in the pictures below? \n\nIf I have a transition like $\\alpha\\rightarrow\\beta$ surrounded by transitions coupled to a single temperature like on the left diagram, it seems reasonable to me to calculate the availa... |
[
{
"from": "human",
"value": "I am currently dealing with the perturbation theory. For the moment in my lectures we are considering the time independent perturbation theory. Degeneracy might be relevant or not. I have a set of questions, which deal more with an intuitive understanding of this theory:\n\nWhy ... |
[
{
"from": "human",
"value": "The following reaction occurs:\\n\\n\\[ \\n2 \\, \\text{Cp}(\\text{CO})_3\\text{Mo-H} + \\text{PhC}(\\text{CH}_3)=\\text{CH}_2 \\rightarrow [\\text{Cp}(\\text{CO})_3\\text{Mo}]_2 + \\text{PhCH}(\\text{CH}_3)_2 \\n\\]\\n\\nOBSERVATIONS\\n\\n1) Second order kinetics are observed, ... |
[
{
"from": "human",
"value": "What is a necessary but not a sufficient condition for optical activity? What is the necessary and sufficient condition for enantiomerism? What conditions must be met for the observation of optical activity?"
},
{
"from": "gpt",
"value": "Let's address each question ... |
[
{
"from": "human",
"value": "3-96 Imagine a mutation that inactivates the site on Cdk that binds to Rb. What would be the effect of this mutation on the reaction in which Cdk phosphorylates Rb?\\nA. A large decrease in \\(K_m\\)\\nB. A large increase in \\(K_m\\)\\nC. A large decrease in \\(V_{max}\\)\\nD. ... |
[
{
"from": "human",
"value": "I'm trying to find the component equation of motion for the action in a paper. The action for the system is,\n$$S=\\frac{m_P^2}{8\\pi}\\int d^4x\\sqrt{-g}\\bigg(\\frac{R}{2}-\\frac{1}{2}\\partial_\\mu\\phi\\partial^\\mu\\phi+\\alpha\\phi\\mathcal{G}\\bigg),$$\nwhere $\\mathcal{G... |
[
{
"from": "human",
"value": "(a) Derive from Coulomb's law and the simple quantization of angular momentum, the energy levels of the hydrogen atom.\\n\\n(b) What gives rise to the doublet structure of the optical spectra from sodium?"
},
{
"from": "gpt",
"value": "Certainly! Let's address each p... |
[
{
"from": "human",
"value": "Let's say we have light contained in a cavity (of initial length $L$) and then instantaneously remove the second mirror, thus removing the barrier between the first and a third mirror which is some further distance away (say $L$ again). If the light was on resonance before the ... |
[
{
"from": "human",
"value": "When we use Gauss' law to derive expressions for the electric field, we usually exploit certain symmetries to ensure that the $E$ term is constant and pulls out of the electric flux integral. For example, to calculate the electric field due to a point charge, we can use a spheri... |
[
{
"from": "human",
"value": "I am interested in this approach, and came accross this book by Leigh Page (\"Chairman of Mathematical Physics at the Sloane Physics Laboratory of Yale University for three dacades\" by Wikipedia). This book is available from archive.org to read for free ( published by 1922; htt... |
[
{
"from": "human",
"value": "The following atomic masses have been determined (in amu):\\n1. \\(^7_3\\text{Li} \\quad 7.0182\\)\\n2. \\(^7_4\\text{Be} \\quad 7.0192\\)\\n\\n(2) \\[\\n\\begin{array}{ccc}\\n\\frac{13}{6} \\text{C} & 13.0076 \\\\\\n\\frac{13}{7} \\text{N} & 13.0100 \\\\\\n\\end{array}\\n\\]\\n... |
[
{
"from": "human",
"value": "Select the chiral atoms in each of the following compounds: Cholesterol (a) There are eight chiral C's: three C's attached to a CH3 group, four C's attached to lone H's, and one C attached to OH. (b) Since N is bonded to four different groups; it is a chiral center, as is the C ... |
[
{
"from": "human",
"value": "Nitrogen is pictured in electron dot symbols as \\(:\\overset{\\cdot\\cdot}{N}\\) with one pair and three single electrons. Which of the following are also correct symbols for nitrogen? \\(:N\\), \\(\\overset{\\cdot}{N}:\\), \\(:\\overset{\\cdot}{N}\\), \\(:N:\\)."
},
{
... |
[
{
"from": "human",
"value": "This reaction does not, in fact, stop here as the two ions produced (charge conservation requires one cation and one anion in this first reaction) now react with each other to form the product of the reaction. This reaction is pretty obvious as the anion is the nucleophile and t... |
[
{
"from": "human",
"value": "What is the smallest number of carbon atoms possible in a molecule of (a) a ketone, (b) an aldehyde, and (c) an aromatic hydrocarbon?"
},
{
"from": "gpt",
"value": "Let's analyze each part step by step:\n\n---\n\n### (a) Smallest number of carbon atoms in a **ketone*... |
[
{
"from": "human",
"value": "I'm currently studying String theory by Becker& Becker, Schwarz textbook. The exercise 2.3 consists in verifying diffeomorphism invariance of einbein action wich is given by\n$$ S_0 = \\frac{1}{2} \\int d\\tau (e^{-1}\\dot{X}^2 - m^2e), \\ e= e(\\tau) \\tag1 $$\nsuch that under ... |
[
{
"from": "human",
"value": "Use \\sinh kt = \\frac{e^t - e^{-x}}{2} and linearity to show that \\mathcal{L}\\{ \\sinh kt \\} = \\frac{k}{s^2-k^2}"
},
{
"from": "gpt",
"value": "Given the definition and using linearity properties of the Laplace transform, we want to show:\n\n\\[\n\\mathcal{L}\\{... |
[
{
"from": "human",
"value": "Theoretical calculations at the ab initio level (HF/4-31G) indicate a pyramidal geometry at carbon in the methyl and ethyl anions. The optimum H-C-H angle in these two carbanions was calculated to be 97°−100°. An interesting effect is observed in that the PA (basicity) of methyl... |
[
{
"from": "human",
"value": "3.52 (a) When (R)-1-phenylethanol is heated with HCOOH, inactive formate ester is obtained. Give the explanation with the mechanism of the reaction.\\n\\n(b) When (R)-sec-butyl methyl ether is treated with HI then the ether is transformed into the corresponding alcohol with the ... |
[
{
"from": "human",
"value": "\\text{2HF} \\rightarrow \\text{H}_2 \\text{F}_2 \\\\\\n\\text{3HF} \\rightarrow \\text{H}_3 \\text{F}_3\\n\\na - (2x + 3y) \\quad x \\quad a - (3y + 2x) \\quad y\\n\\nFrom question,\\n\\n\\frac{y}{a - (2x + 3y)} = \\frac{1}{4} \\tag{1}\\n\\nand \\left[ a - (2x + 3y) \\right] : ... |
[
{
"from": "human",
"value": "I was trying to prove that kinetic energy is constant in a rigid body undergoing some arbitrary rotation around the origin in a 3D space, and I ended up proving a stronger statement: that the norm of the linear velocity of any one particle is constant.\nIs this true?\nUPDATE:\nI... |
[
{
"from": "human",
"value": "The compounds most reactive in the Williamson ether synthesis are also most reactive in any SN2 reaction (review Chapter 11 if necessary). The hierarchy of reactivity is as follows: CH3CH2Br (primary halide) > secondary halide >> aryl halide (not reactive). (b) CH3CH2Br is consi... |
[
{
"from": "human",
"value": "The evidence that convinced chemists about these two mechanisms is kinetic: it relates to the rate of the reactions. It was discovered, chiefly by Hughes and Ingold in the 1930s, that some nucleophilic substitutions are first-order, that is, the rate depends only on the concentr... |
[
{
"from": "human",
"value": "Notice that the alkyl halide has one less carbon than the target carboxylic acid because the alkyl halide will obtain a carbon from the cyanide ion. \na. CH3CH2CH2Br \nb. CH3CHCH2Br \n\nWhich alkyl halide has one less carbon than the target carboxylic acid?"
},
{
"fro... |
[
{
"from": "human",
"value": "Find the number of isomeric forms in which \\([\\text{Co(NH}_3)_5\\text{Cl}]^{2+}\\) ion can occur."
},
{
"from": "gpt",
"value": "Let's analyze the complex \\([\\text{Co(NH}_3)_5\\text{Cl}]^{2+}\\).\n\n---\n\n### Given:\n\n- Coordination complex: \\([\\text{Co(NH}_3... |
[
{
"from": "human",
"value": "The pressure of propane versus density at 400 K can be fit by the expression\\n\\nP/bar = 33.258(ρ/mol · L^{-1}) - 7.5884(ρ/mol · L^{-1})^2 + 1.0306(ρ/mol · L^{-1})^3 - 0.058757(ρ/mol · L^{-1})^4 - 0.0033566(ρ/mol · L^{-1})^5 + 0.000060696(ρ/mol · L^{-1})^6\\n\\nfor 0 ≤ ρ/mol · ... |
[
{
"from": "human",
"value": "Which of the following is the correct ranking in decreasing order of relative Boiling Point of carbonyl containing compounds? (a) primary amide > carboxylic acid >> ester ~ acyl chloride ~ aldehyde ~ ketone (b) ester > carboxylic acid >> amide ~ acyl chloride ~ aldehyde ~ keto... |
[
{
"from": "human",
"value": "I am a computer graphics guy in the area of physically-based rendering and recently I've been searching on the net to figure out how physical is Physically Based Rendering (PBR). The nature of the question lies somewhere between pure physics and pure graphics, so I'm hoping I fi... |
[
{
"from": "human",
"value": "Would it be possible through a clever arrangement of solar dishes, lenses and mirrors etc, to create fusion at the focal point?\nImagine you arrange your solar dishes, lenses and mirrors in such a way, that the final stage would be lenses fixed up in the air, surrounding the tar... |
[
{
"from": "human",
"value": "The bases of nucleotides and polynucleotides are “information symbols.” Their central role in providing information content to DNA and RNA is clear. What advantages might bases as “information symbols” bring to the roles of nucleotides in metabolism?"
},
{
"from": "gpt",... |
[
{
"from": "human",
"value": "From what i read:\n\nNormal force is the force that prevents objects from passing through eachother,which is the force of the repulsion\nfrom the charge.\n\nThe normal force will get as large as required to prevent objects from penetrating each other.\n\n\n\nMy question is about... |
[
{
"from": "human",
"value": "I am a platform diver. I am trying to figure out how deep in the water I go depending on which platform I dive from.\nThe platforms are 1m, 3m, 5m, 7.5m and 10m above the water surface.\nBy ignoring air resistance (we assume that I do not do any tricks) I can easily compute the ... |
[
{
"from": "human",
"value": "Years ago I read something that said in crystals \"atoms have finite positions along the crystal lattice.\"\nWhat I took that to mean was that in any crystal structure, atoms have a finite number of possible positions. Which is what I want to find out here.\nAfter searching imag... |
[
{
"from": "human",
"value": "Assertion: F^- ion has highest hydrated radius among the other halide ions. Reason: Ionic radius of F^- is smallest in the periodic table."
},
{
"from": "gpt",
"value": "Let's analyze the Assertion and Reason carefully:\n\n**Assertion:** F⁻ ion has the highest hydrat... |
[
{
"from": "human",
"value": "Here is a thought experiment.\nStart with a low-frequency maser, say a frequency of 1 hertz.\nPut a circular fan in the way of the maser, with blades that cover half the area they rotate through. Run it fast enough that the maser is blocked for half a second and then the radiati... |
[
{
"from": "human",
"value": "There are claims that the Ross-Littlewood paradox could be simulated in physics.\nSee https://stats.stackexchange.com/q/315502/ and in particular Paul's answer there.\nAlso a solution of the Einstein-Podolsky-Rosen paradox using extended probabilities as invented by Dirac, Bartl... |
[
{
"from": "human",
"value": "Cholesterol is an essential component of the plasma membrane, but people who have very high levels of cholesterol in their blood (hypercholesterolemia) tend to have heart attacks. Blood cholesterol is carried in the form of cholesterol esters in low-density lipoprotein (LDL) par... |
[
{
"from": "human",
"value": "When an aqueous solution of aniline is treated with bromine-water, symmetrical tribromo-aniline is precipitated. What precipitate is formed when an aqueous solution of aniline is treated with bromine-water?"
},
{
"from": "gpt",
"value": "When **aniline (C6H5NH2)** is... |
[
{
"from": "human",
"value": "The given question says , Two smalls discs A and B of masses m1 and M2 connected by a light inextensible string of length l are placed on a frictionless horizontal floor. Disc A is held at rest and the disc B is projected to move around the disc A with a constant speed u on a ci... |
[
{
"from": "human",
"value": "Write bond-line structural formulas for (a) two constitutionally isomeric primary alkyl bromides with the formula C₄H₉Br, (b) a secondary alkyl bromide, and (c) a tertiary alkyl bromide with the same formula. Build hand-held molecular models for each structure and examine the di... |
[
{
"from": "human",
"value": "Distinguish explicitly between the rate of the chemical reaction and the rate constant for the reaction."
},
{
"from": "gpt",
"value": "Certainly! Here's an explicit distinction between the **rate of a chemical reaction** and the **rate constant** for the reaction:\n... |
[
{
"from": "human",
"value": "Consider a real scalar field\n\\begin{equation}\n\\phi(x)=\\int\\frac{d^3p}{(2\\pi)^3}\\frac{1}{\\sqrt{2E_p}}\\left(a_pe^{-ip\\cdot x}+a_p^{\\dagger}e^{ip\\cdot x} \\right).\n\\end{equation}\nIn Chapter 2 of Peskin, right after Eq. 2.64, we have the form of the hamiltonian for a... |
[
{
"from": "human",
"value": "Suppose heavy particle or body (\"billiard ball\") is accelerated with very thin and very rigid (not absolutely rigid) rod of infinitesimal (not zero) mass (\"cue stick\")\n\nAcceleration is constant in relativity sense, i.e. hyperbolic motion in stationary reference frame. Mass... |
[
{
"from": "human",
"value": "Explain the fact that trans-4-tert-butylcyclohexyl tosylate undergoes bimolecular elimination with the bases bromide and thiophenolate, although not with the much stronger base ethoxide."
},
{
"from": "gpt",
"value": "Let's analyze the problem step-by-step:\n\n---\n\... |
[
{
"from": "human",
"value": "So the Lieb-Robinson bound of 1972 derives an emergent maximum speed $v \\ll c$ of the propagation of quantum information under time evolution generated by some local Hamiltonian $H(t)$. Basically, transmitting quantum information over a distance $L$ or preparing an entangled / ... |
[
{
"from": "human",
"value": "Name (a) C6H5SO2OCH3, (b) C6H5SO2NH2, (c) p-BrC6H4CO2Cl."
},
{
"from": "gpt",
"value": "Let's identify each compound and provide its correct IUPAC or common name:\n\n---\n\n**(a) C₆H₅SO₂OCH₃**\n\n- C₆H₅ = phenyl group (benzene ring)\n- SO₂O = sulfonate linkage (sulfo... |
[
{
"from": "human",
"value": "How can I show that the non relativistic second quantization hamiltonian \n\\begin{equation}\n\\hat{H}=\\lmoustache d^3x \\hat{\\psi}^\\dagger_\\alpha(x) T(x)\\hat{\\psi}^\\dagger(x)+\\frac{1}{2}\\lmoustache d^3x\\lmoustache d^3x' \\hat{\\psi}^\\dagger_\\alpha(x) \\hat{\\psi}_\\... |
[
{
"from": "human",
"value": "Two drops of phenolphthalein solution was added to 40.0 mL of an HCl solution. This solution was titrated with 0.1 M NaOH solution. When 30.0 mL of base had been added, part of the solution turned pink, but the colour disappeared upon mixing the solution. Addition of NaOH soluti... |
[
{
"from": "human",
"value": "In a 1,3-electron pair displacement operation, one atom with a pair of nonbonding electrons forms a bond with a second atom and displaces a pair of bonding electrons to a third atom. The third general operation is the 1,3-electron pair displacement operation. This reaction invol... |
[
{
"from": "human",
"value": "Dehydrohalogenation of cycloalkyl halides lead exclusively to cis cycloalkenes when the ring has fewer than ten carbons. As the ring becomes larger, it can accommodate either a cis or a trans double bond, and large-ring cycloalkyl halides give mixtures of cis and trans cycloalke... |
[
{
"from": "human",
"value": "\nI would in general like to understand how to derive the low energy metrics to describe D-brane configurations. Any pedagogic reference which explains the method?\n\nIn particular I have in mind these two facts, \n(1) For N coincident D3 branes in IIB it seems that the metric i... |
[
{
"from": "human",
"value": "Ergocalciferol (so-called \"Vitamin D2\"), C28H44O, an alcohol, gives C28H52O upon catalytic hydrogenation. How many rings does each of the following contain? (e) How many double bonds does ergocalciferol contain?"
},
{
"from": "gpt",
"value": "Let's analyze ergocalc... |
[
{
"from": "human",
"value": "While trying to provide an answer to this question, I got confused with something which I think might be the root of the problem. In the paper the OP was reading, the author writes $$\\frac{d\\hat{A}}{dt}=\\frac{\\partial \\hat{A}}{\\partial t}+\\sum_k \\frac{\\partial \\hat{A}}... |
[
{
"from": "human",
"value": "I see several related questions, mostly taking the standard position/interpretation that complex-valued amplitudes aren't \"physically real\" (though their imaginary components do participate in interference effects that are ultimately experimentally observable), whereas real-va... |
[
{
"from": "human",
"value": "The molecular formula tells us that the compound does not have any degrees of unsaturation. Therefore, the oxygen must be the oxygen of either an ether or an alcohol. Because there are no signals that integrate to one proton, we can conclude that the compound is an ether. The tr... |
[
{
"from": "human",
"value": "A technologist neglects to give a patient potassium perchlorate before injection with 20 mCi of \\(^{99m}\\text{Tc}\\) pertechnetate. How will this affect the static brain images taken at 1 hour after injection?\\n a. thyroid activity may be seen\\n b. choroid plexus may be ... |
[
{
"from": "human",
"value": "A and X are two common non-metallic elements. The sum of their atomic numbers is 22, and the sum of their valence layer electron counts is 10. Under certain conditions, AX, AX3 (a common Lewis acid), A2X4 and A4X4 can be generated. Write the equation for the reaction of AX3 with... |
[
{
"from": "human",
"value": "The signals in the 'H NMR spectrum are all singlets, indicating that none of the protons that give these signals have any neighboring protons. The singlet (2.4 ppm) that integrates to 1 proton is the proton of the terminal alkyne. The two remaining signals (3.4 and 4.1 ppm) inte... |
[
{
"from": "human",
"value": "I have heard from several physicists that the Kapustin-Witten topological twist of $N=4$ 4-dimensional Yang-Mills theory (\"the Geometric Langlands twist\") is not expected to give\nrise to fully defined topological field theory in the sense that, for example, its partition func... |
[
{
"from": "human",
"value": "\\( \\text{K}_2\\text{CrO}_4 \\) is slowly added to a solution that is 0.0200 M in Pb(NO\\(_3\\))\\(_2\\) and 0.0200 M in Ba(NO\\(_3\\))\\(_2\\). \\n (a) Which ion precipitates first? \\n (b) What will be its concentration when the second ion begins to precipitate?"
},... |
[
{
"from": "human",
"value": "In which type of excitons, tight binding approximation can be applied and why?"
},
{
"from": "gpt",
"value": "**Answer:**\n\nThe **tight binding approximation** can be applied to **Frenkel excitons**, which are also called small-radius excitons.\n\n---\n\n### Explana... |
[
{
"from": "human",
"value": "Q:If we know that the acceleration vectors of all points of the rigid body are equal to each other at all points of time, can we conclude that the body is undergoing pure translational motion?\nI recently learnt that both the necessary and sufficient condition for a Rigid body t... |
[
{
"from": "human",
"value": "The action of Witten's topological sigma model (defined on a worldsheet, $\\Sigma$, with target space an almost complex manifold denoted $X$) takes the form \n$$\nS=\\int d^2\\sigma\\big(-\\frac{1}{4}H^{\\alpha i}H_{\\alpha i}+H^{\\alpha }_i\\partial_{\\alpha}u^i+\\ldots\\big), ... |
[
{
"from": "human",
"value": "By referring to one-electron \\( s \\) states try to derive the correction to the unperturbed energy value due to \\( H_{spin-orbit} \\), making a remark on what has to be expected."
},
{
"from": "gpt",
"value": "Let's analyze the correction to the energy of one-elec... |
[
{
"from": "human",
"value": "Consider two identical sources $S_1$ and $S_2$ of waves, separated by a distance $\\ell$ (as shown in the figure).\n\nThe sources produce waves in opposite directions(and towards each other). Now, suppose we wish to derive the equation for the standing wave produced.\nLet us tak... |
[
{
"from": "human",
"value": "Let's suppose I'm on a carousel rotating with a speed $\\omega$ and start running on it in the opposite direction with a speed $v$ such that $\\omega r=-v$ where $r$ is the distance between me and the center of the carousel.\nWhat are the forces that act on me? Do I feel Corioli... |
[
{
"from": "human",
"value": "Find the number of molecule(s) which is/are planar as well as polar:\\n\\n\\( \\overset{\\text{H}}{\\text{H}}—\\overset{\\text{C}}{\\text{C}}—\\overset{\\text{H}}{\\text{H}} \\)\\n\\n\\( \\overset{\\text{C}}{\\text{H}}—\\overset{\\text{C}}{\\text{C}}—\\overset{\\text{Cl}}{\\text... |
[
{
"from": "human",
"value": "If i look de Broglie equation\n$$\\lambda = \\frac{h}{m\\gamma v}$$ , where $\\gamma$ is Lorentz gamma factor $$ \\gamma = 1/\\sqrt{1-(v/c)^2} $$\nand change that to the equation\nfor frequency $f = v/\\lambda$, i get following equation:\n$$ f = m\\gamma v^2/h $$ .\nWhat is inte... |
[
{
"from": "human",
"value": "My brother wants to mount his T.V. to the wall and wants to know if his drywall anchors will be enough. We haven't done any free body diagram analysis in a long time so we just want to know if what we did is right.\nThis is the diagram:\n\nSo it is a metal plaque with 4 screw ho... |
[
{
"from": "human",
"value": "Seeds containing 25 per cent by mass of oil are extracted in a countercurrent plant and 90 per cent of the oil is to be recovered in a solution containing 50 per cent of oil. It has been found that the amount of solution removed in the underflow in association with every kilogra... |
[
{
"from": "human",
"value": "(For the purposes of a science-fiction story where the author is attempting to have as much basis in fact as possible) if one were to create or make use of a Morris-Thorne or similar traversable wormhole and accelerate one end to modify it to be a \"time machine\", would one sim... |
[
{
"from": "human",
"value": "The term 'chirality' is derived from the Greek word χειρ (‘kheir'), meaning palm. Like your hands, chiral molecules are molecules which have non-superimposable mirror images. They usually (but not always) contain chiral centres, which are often defined as carbon atoms with four ... |
[
{
"from": "human",
"value": "Muscles contain creatine phosphate (CP) as an energy buffer to maintain the levels of ATP in the initial stages of exercise. Creatine phosphate can transfer its phosphate to ADP to generate creatine (C) and ATP, with a ΔG° of -3.3 kcal/mole.\\n\\nCP + ADP → C + ATP ΔG° = -3.3 k... |
[
{
"from": "human",
"value": "Let's consider 2 events in an inertial system $S$:\n$$x_1=(0,0,0,0) \\quad \\quad \\quad x_2=( \\Delta t, \\Delta x,0,0)$$\nIf we assume the two events occur in the same place we have: $\\Delta \\bar{t}= \\gamma \\Delta t$ for every other inertial system, also known as time dila... |
[
{
"from": "human",
"value": "According to standard quantum mechanics, Hilbert space is defined over the complex numbers, and amplitudes in a superposition can take on values with arbitrarily small magnitude. This probably does not trouble non-realist interpretations of the wavefunction, or explicit wave fun... |
[
{
"from": "human",
"value": "Mean field theory applied to spin-chains, where the ground state is assumed a product state and the energy is variationally minimized, is one of the tools in my toolkit. The examples I give in this question make me wonder if it behaves inappropriately under the addition of quart... |
[
{
"from": "human",
"value": "When ethyl acetate in dilute aqueous solution is heated in the presence of a small amount of acid, it decomposes according to the equation\\n\\n\\[\\n\\text{CH}_3\\text{COOC}_2\\text{H}_5 + \\text{H}_2\\text{O} \\rightarrow \\text{CH}_3\\text{COOH} + \\text{C}_2\\text{H}_5\\text... |
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