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 # Video files - compressed
 *.mp4 filter=lfs diff=lfs merge=lfs -text
 *.webm filter=lfs diff=lfs merge=lfs -text
+Smith_Smith_2015.chunks.json filter=lfs diff=lfs merge=lfs -text
+Text_Book_of_Microbiology.chunks.json filter=lfs diff=lfs merge=lfs -text
+clairvoyance.ipynb.chunks.json filter=lfs diff=lfs merge=lfs -text

F814BC5915875384820.chunks.json

@@ -0,0 +1,138 @@
+[
+  {
+    "page_content": "- 1-1. Blackbody Radiation Could Not Be Explained by Classical Physics 2\n- 1-2. Planck Used a Quantum Hypothesis to Derive the Blackbody Radiation Law 4\n- 1-3. Einstein Explained the Photoelectric Effect with a Quantum Hypothesis 7\n- 1-4. The Hydrogen Atomic Spectrum Consists of Several Series of Lines 10\n- 1-5. The Rydberg Formula Accounts for All the Lines in the Hydrogen Atomic Spectrum 13\n- 1-6. Louis de Broglie Postulated That Matter Has Wavelike Properties 15\n- 1-7. de Broglie Waves Are Observed Experimentally 16\n- 1-8. The Bohr Theory of the Hydrogen Atom Can Be Used to Derive the Rydberg Formula 18\n- 1-9. The Heisenberg Uncertainty Principle States That the Position and the Momentum of a Particle Cannot Be Specified Simultaneously with Unlimited Precision 23  \nProblems 25\n\nProblems 35",
+    "metadata": {
+      "Header 1": "**CHAPTER 1** I The Dawn of the Quantum Theory",
+      "Header 2": "Blackbody Radiation Could Not Be Explained by Classical Physics",
+      "is_merged_section": true,
+      "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/F814BC5915875384820.pdf"
+    }
+  },
+  {
+    "page_content": "- 2-1. The One-Dimensional Wave Equation Describes the Motion of a Vibrating String 39\n- 2-2. The Wave Equation Can Be Solved by the Method of Separation of Variables 40\n- 2-3. Some Differential Equations Have Oscillatory Solutions 44\n- 2-4. The General Solution to the Wave Equation Is a Superposition of Normal Modes 46\n- 2-5. A Vibrating Membrane Is Described by a Two-Dimensional Wave Equation 49  \nProblems 54\n\nProblems 70",
+    "metadata": {
+      "Header 1": "**CHAPTER 1** I The Dawn of the Quantum Theory",
+      "Header 2": "Planck Used a Quantum Hypothesis to Derive the Blackbody Radiation Law",
+      "is_merged_section": true,
+      "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/F814BC5915875384820.pdf"
+    }
+  },
+  {
+    "page_content": "- **3-1.** The Schrödinger Equation Is the Equation for Finding the Wave Function of a Particle 73\n- **3-2.** Classical-Mechanical Quantities Are Represented by Linear Operators in Ouantum Mechanics 75\n- 3-3. The Schrödinger Equation Can Be Formulated As an Eigenvalue Problem 77\n- **3-4.** Wave Function's Have a Probabilistic Interpretation 80\n- **3-5.** The Energy of a Particle in a Box Is Quantized 81\n- 3-6. Wave Functions Must Be Normalized 84\n- 3-7. The Average Momentum of a Particle in a Box Is Zero 86\n- **3-8.** The Uncertainty Principle Says That  $\\sigma_n \\sigma_r > \\hbar/2$  88\n- **3-9.** The Problem of a Particle in a Three-Dimensional Box Is a Simple Extension of the One-Dimensional Case 90  \nProblems 96  \n#### MATHCHAPTER C / Vectors 105  \nProblems 113\n\n- 4-1. The State of a System Is Completely Specified by Its Wave Function 115\n- 4-2. Quantum-Mechanical Operators Represent Classical-Mechanical Variables 118\n- **4-3.** Observable Quantities Must Be Eigenvalues of Quantum Mechanical Operators 122\n- **4-4.** The Time Dependence of Wave Functions Is Governed by the Time-Dependent Schrödinger Equation 125\n- **4-5.** The Eigenfunctions of Quantum Mechanical Operators Are Orthogonal 127\n- **4-6.** The Physical Quantities Corresponding to Operators That Commute Can Be Measured Simultaneously to Any Precision 131  \nProblems 134  \n![](_page_3_Picture_22.jpeg)",
+    "metadata": {
+      "Header 1": "**CHAPTER 1** I The Dawn of the Quantum Theory",
+      "Header 2": "Einstein Explained the Photoelectric Effect",
+      "is_merged_section": true,
+      "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/F814BC5915875384820.pdf"
+    }
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+  {
+    "page_content": "- 1-1. Blackbody Radiation Could Not Be Explained by Classical Physics 2\n- 1-2. Planck Used a Quantum Hypothesis to Derive the Blackbody Radiation Law 4\n- 1-3. Einstein Explained the Photoelectric Effect with a Quantum Hypothesis 7\n- 1-4. The Hydrogen Atomic Spectrum Consists of Several Series of Lines 10\n- 1-5. The Rydberg Formula Accounts for All the Lines in the Hydrogen Atomic Spectrum 13\n- 1-6. Louis de Broglie Postulated That Matter Has Wavelike Properties 15\n- 1-7. de Broglie Waves Are Observed Experimentally 16\n- 1-8. The Bohr Theory of the Hydrogen Atom Can Be Used to Derive the Rydberg Formula 18\n- 1-9. The Heisenberg Uncertainty Principle States That the Position and the Momentum of a Particle Cannot Be Specified Simultaneously with Unlimited Precision 23  \nProblems 25\n\nProblems 35\n\n- 2-1. The One-Dimensional Wave Equation Describes the Motion of a Vibrating String 39\n- 2-2. The Wave Equation Can Be Solved by the Method of Separation of Variables 40\n- 2-3. Some Differential Equations Have Oscillatory Solutions 44\n- 2-4. The General Solution to the Wave Equation Is a Superposition of Normal Modes 46\n- 2-5. A Vibrating Membrane Is Described by a Two-Dimensional Wave Equation 49  \nProblems 54\n\nProblems 70\n\n- **3-1.** The Schrödinger Equation Is the Equation for Finding the Wave Function of a Particle 73\n- **3-2.** Classical-Mechanical Quantities Are Represented by Linear Operators in Ouantum Mechanics 75\n- 3-3. The Schrödinger Equation Can Be Formulated As an Eigenvalue Problem 77\n- **3-4.** Wave Function's Have a Probabilistic Interpretation 80\n- **3-5.** The Energy of a Particle in a Box Is Quantized 81\n- 3-6. Wave Functions Must Be Normalized 84\n- 3-7. The Average Momentum of a Particle in a Box Is Zero 86\n- **3-8.** The Uncertainty Principle Says That  $\\sigma_n \\sigma_r > \\hbar/2$  88\n- **3-9.** The Problem of a Particle in a Three-Dimensional Box Is a Simple Extension of the One-Dimensional Case 90  \nProblems 96  \n#### MATHCHAPTER C / Vectors 105  \nProblems 113\n\n- 4-1. The State of a System Is Completely Specified by Its Wave Function 115\n- 4-2. Quantum-Mechanical Operators Represent Classical-Mechanical Variables 118\n- **4-3.** Observable Quantities Must Be Eigenvalues of Quantum Mechanical Operators 122\n- **4-4.** The Time Dependence of Wave Functions Is Governed by the Time-Dependent Schrödinger Equation 125\n- **4-5.** The Eigenfunctions of Quantum Mechanical Operators Are Orthogonal 127\n- **4-6.** The Physical Quantities Corresponding to Operators That Commute Can Be Measured Simultaneously to Any Precision 131  \nProblems 134  \n![](_page_3_Picture_22.jpeg)\n\nProblems 153\n\n- **5-1.** A Harmonic Oscillator Obeys Hooke's Law 157\n- **5-2.** The Equation for a Harmonic-Oscillator Model of a Diatomic Molecule Contains the Reduced Mass of the Molecule 161\n- **5-3.** The Harmonic-Oscillator Approximation Results from the Expansion of an Internuclear Potential Around Its Minimum 163\n- \\* 5-4. The Energy Levels of a Quantum-Mechanical Harmonic Oscillator Are  $E_v = \\hbar\\omega(v+\\frac{1}{2})$  with  $v=0,\\ 1,\\ 2,\\ \\dots$  166\n- 5-5. The Harmonic Oscillator Accounts for the Infrared Spectrum of a Diatomic Molecule 167\n- 5-6. The Harmonic-Oscillator Wave Functions Involve Hermite Polynomials 169\n- **5-7.** Hermite Polynomials Are Either Even or Odd Functions 172\n- **5-8** The Energy Levels of a Rigid Rotator Are  $E = \\hbar^2 J(J+1)/2I$  173  \n/~The Rigid Rotator Is a Model for a Rotating Diatomic Molecule 177 Problems 1 79\n\n- 6-1. The Schrodinger Equation for the Hydrogen Atom Can Be Solved Exactly 191\n- 6-2. The Wave Functions of a Rigid Rotator Are Called Spherical Harmonics 193\n- 6-3. The Precise Values of the Three Components of Angular Momentum Cannot Be Measured Simultaneously 200\n- 6-4. Hydrogen Atomic Orbitals Depend upon Three Quantum Numbers 206\n- 6-5. *s* Orbitals Are Spherically Symmetric 209\n- 6-6. There Are Three *p*Orbitals for Each Value of the Principal Quantum Number, *<sup>n</sup>*~ 2 213\n- 6-7. The Schrodinger Equation for the Helium Atom Cannot Be Solved Exactly 219 Problems 220  \n#### MATHCHAPTER E I Determinants 231  \nProblems 238\n\n- <sup>~</sup>7-1. The Variational Method Provides an Upper Bound to the Ground-State Energy of a System 241\n- 7-2. A Trial Function That Depends Linearly on the Variational Parameters Leads to a Secular Determinant 249\n- 7-3. Trial Functions Can Be Linear Combinations of Functions That Also Contain Variational Parameters 256\n- <sup>~</sup>7-4. Perturbation Theory Expresses the Solution to One Problem in Terms of Another Problem Solved Previously 257  \nProblems 2 61  \n#### CHAPTER 8 I Multielectron Atoms 275  \n- 8-1. Atomic and Molecular Calculations Are Expressed in Atomic Units 275\n- 8-2. Both Perturbation Theory and the Variational Method Can Yield Excellent Results for Helium 278\n- 8-3. Hartree-Fock Equations Are Solved by the Self-Consistent Field Method 282\n- 8-4. An Electron Has an Intrinsic Spin Angular Momentum 284\n- 8-5. Wave Functions Must Be Antisymmetric in the Interchange of Any Two Electrons 285\n- 8-6. Antisymmetric Wave Functions Can Be Represented by Slater Determinants 288\n- 8-7. Hartree-Fock Calculations Give Good Agreement with Experimental Data 290\n- 8-8. A Term Symbol Gives a Detailed Description of an Electron Configuration 292\n- @jrhe Allowed Values of J are *L* + *S, L* + *S-* 1, 0 0 0, IL- Sl 296\n- 8-10. Hund's Rules Are Used to Determine the Term Symbol of the Ground Electronic State 301\n- -! 8-11. Atomic Term Symbols Are Used to Describe Atomic Spectra 302 Problems 308  \n- **@-1.** The Born-Oppenheimer Approximation Simplifies the Schrodinger Equation for Molecules 323\n- **9-2.** Hi Is the Prototypical Species of Molecular-Orbital Theory 325\n- 9-3. The Overlap Integral Is a Quantitative Measure of the Overlap of Atomic Orbitals Situated on Different Atoms 327\n- **9-4.** The Stability of a Chemical Bond Is a Quantum-Mechanical Effect 329\n- 9-5. The Simplest Molecular Orbital Treatment of Hi Yields a Bonding Orbital and an Antibonding Orbital 333\n- **9-6.** A Simple Molecular-Orbital Treatment of H2 Places Both Electrons in a Bonding Orbital 336\n- 9-7. Molecular Orbitals Can Be Ordered According to Their Energies 336\n- **9-8.** Molecular-Orbital Theory Predicts That a Stable Diatomic Helium Molecule Does Not Exist 341\n- **9-9.** Electrons Are Placed into Molecular Orbitals in Accord with the Pauli Exclusion Principle 342\n- **9-10.** Molecular-Orbital Theory Correctly Predicts That Oxygen Molecules Are Paramagnetic 344\n- **9-11.** Photoelectron Spectra Support the Existence of Molecular Orbitals 346\n- **9-12.** Molecular-Orbital Theory Also Applies to Heteronuclear Diatomic Molecules 346\n- **9-13.** An SCF-LCAO-MO Wave Function Is a Molecular Orbital Formed from a Linear Combination of Atomic Orbitals and Whose Coefficients Are Determined Self-Consistently 349\n- **9-14.** Electronic States of Molecules Are Designated by Molecular Term Symbols 355\n- **9-15.** Molecular Term Symbols Designate the Symmetry Properties of Molecular Wave Functions 358\n- **9-16.** Most Molecules Have Excited Electronic States 360",
+    "metadata": {
+      "Header 1": "**MATHCHAPTER A** I Complex Numbers 31",
+      "Header 2": "Introduction to Complex Numbers",
+      "is_merged_section": true,
+      "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/F814BC5915875384820.pdf"
+    }
+  },
+  {
+    "page_content": "- 2-1. The One-Dimensional Wave Equation Describes the Motion of a Vibrating String 39\n- 2-2. The Wave Equation Can Be Solved by the Method of Separation of Variables 40\n- 2-3. Some Differential Equations Have Oscillatory Solutions 44\n- 2-4. The General Solution to the Wave Equation Is a Superposition of Normal Modes 46\n- 2-5. A Vibrating Membrane Is Described by a Two-Dimensional Wave Equation 49  \nProblems 54",
+    "metadata": {
+      "Header 2": "**MATHCHAPTER A** I Complex Numbers 31",
+      "Header 3": "**CHAPTER** 2 I The Classical Wave Equation 39",
+      "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/F814BC5915875384820.pdf"
+    }
+  },
+  {
+    "page_content": "- 1-1. Blackbody Radiation Could Not Be Explained by Classical Physics 2\n- 1-2. Planck Used a Quantum Hypothesis to Derive the Blackbody Radiation Law 4\n- 1-3. Einstein Explained the Photoelectric Effect with a Quantum Hypothesis 7\n- 1-4. The Hydrogen Atomic Spectrum Consists of Several Series of Lines 10\n- 1-5. The Rydberg Formula Accounts for All the Lines in the Hydrogen Atomic Spectrum 13\n- 1-6. Louis de Broglie Postulated That Matter Has Wavelike Properties 15\n- 1-7. de Broglie Waves Are Observed Experimentally 16\n- 1-8. The Bohr Theory of the Hydrogen Atom Can Be Used to Derive the Rydberg Formula 18\n- 1-9. The Heisenberg Uncertainty Principle States That the Position and the Momentum of a Particle Cannot Be Specified Simultaneously with Unlimited Precision 23  \nProblems 25\n\nProblems 35\n\n- 2-1. The One-Dimensional Wave Equation Describes the Motion of a Vibrating String 39\n- 2-2. The Wave Equation Can Be Solved by the Method of Separation of Variables 40\n- 2-3. Some Differential Equations Have Oscillatory Solutions 44\n- 2-4. The General Solution to the Wave Equation Is a Superposition of Normal Modes 46\n- 2-5. A Vibrating Membrane Is Described by a Two-Dimensional Wave Equation 49  \nProblems 54\n\nProblems 70\n\n- **3-1.** The Schrödinger Equation Is the Equation for Finding the Wave Function of a Particle 73\n- **3-2.** Classical-Mechanical Quantities Are Represented by Linear Operators in Ouantum Mechanics 75\n- 3-3. The Schrödinger Equation Can Be Formulated As an Eigenvalue Problem 77\n- **3-4.** Wave Function's Have a Probabilistic Interpretation 80\n- **3-5.** The Energy of a Particle in a Box Is Quantized 81\n- 3-6. Wave Functions Must Be Normalized 84\n- 3-7. The Average Momentum of a Particle in a Box Is Zero 86\n- **3-8.** The Uncertainty Principle Says That  $\\sigma_n \\sigma_r > \\hbar/2$  88\n- **3-9.** The Problem of a Particle in a Three-Dimensional Box Is a Simple Extension of the One-Dimensional Case 90  \nProblems 96  \n#### MATHCHAPTER C / Vectors 105  \nProblems 113\n\n- 4-1. The State of a System Is Completely Specified by Its Wave Function 115\n- 4-2. Quantum-Mechanical Operators Represent Classical-Mechanical Variables 118\n- **4-3.** Observable Quantities Must Be Eigenvalues of Quantum Mechanical Operators 122\n- **4-4.** The Time Dependence of Wave Functions Is Governed by the Time-Dependent Schrödinger Equation 125\n- **4-5.** The Eigenfunctions of Quantum Mechanical Operators Are Orthogonal 127\n- **4-6.** The Physical Quantities Corresponding to Operators That Commute Can Be Measured Simultaneously to Any Precision 131  \nProblems 134  \n![](_page_3_Picture_22.jpeg)\n\nProblems 153\n\n- **5-1.** A Harmonic Oscillator Obeys Hooke's Law 157\n- **5-2.** The Equation for a Harmonic-Oscillator Model of a Diatomic Molecule Contains the Reduced Mass of the Molecule 161\n- **5-3.** The Harmonic-Oscillator Approximation Results from the Expansion of an Internuclear Potential Around Its Minimum 163\n- \\* 5-4. The Energy Levels of a Quantum-Mechanical Harmonic Oscillator Are  $E_v = \\hbar\\omega(v+\\frac{1}{2})$  with  $v=0,\\ 1,\\ 2,\\ \\dots$  166\n- 5-5. The Harmonic Oscillator Accounts for the Infrared Spectrum of a Diatomic Molecule 167\n- 5-6. The Harmonic-Oscillator Wave Functions Involve Hermite Polynomials 169\n- **5-7.** Hermite Polynomials Are Either Even or Odd Functions 172\n- **5-8** The Energy Levels of a Rigid Rotator Are  $E = \\hbar^2 J(J+1)/2I$  173  \n/~The Rigid Rotator Is a Model for a Rotating Diatomic Molecule 177 Problems 1 79\n\n- 6-1. The Schrodinger Equation for the Hydrogen Atom Can Be Solved Exactly 191\n- 6-2. The Wave Functions of a Rigid Rotator Are Called Spherical Harmonics 193\n- 6-3. The Precise Values of the Three Components of Angular Momentum Cannot Be Measured Simultaneously 200\n- 6-4. Hydrogen Atomic Orbitals Depend upon Three Quantum Numbers 206\n- 6-5. *s* Orbitals Are Spherically Symmetric 209\n- 6-6. There Are Three *p*Orbitals for Each Value of the Principal Quantum Number, *<sup>n</sup>*~ 2 213\n- 6-7. The Schrodinger Equation for the Helium Atom Cannot Be Solved Exactly 219 Problems 220  \n#### MATHCHAPTER E I Determinants 231  \nProblems 238\n\n- <sup>~</sup>7-1. The Variational Method Provides an Upper Bound to the Ground-State Energy of a System 241\n- 7-2. A Trial Function That Depends Linearly on the Variational Parameters Leads to a Secular Determinant 249\n- 7-3. Trial Functions Can Be Linear Combinations of Functions That Also Contain Variational Parameters 256\n- <sup>~</sup>7-4. Perturbation Theory Expresses the Solution to One Problem in Terms of Another Problem Solved Previously 257  \nProblems 2 61  \n#### CHAPTER 8 I Multielectron Atoms 275  \n- 8-1. Atomic and Molecular Calculations Are Expressed in Atomic Units 275\n- 8-2. Both Perturbation Theory and the Variational Method Can Yield Excellent Results for Helium 278\n- 8-3. Hartree-Fock Equations Are Solved by the Self-Consistent Field Method 282\n- 8-4. An Electron Has an Intrinsic Spin Angular Momentum 284\n- 8-5. Wave Functions Must Be Antisymmetric in the Interchange of Any Two Electrons 285\n- 8-6. Antisymmetric Wave Functions Can Be Represented by Slater Determinants 288\n- 8-7. Hartree-Fock Calculations Give Good Agreement with Experimental Data 290\n- 8-8. A Term Symbol Gives a Detailed Description of an Electron Configuration 292\n- @jrhe Allowed Values of J are *L* + *S, L* + *S-* 1, 0 0 0, IL- Sl 296\n- 8-10. Hund's Rules Are Used to Determine the Term Symbol of the Ground Electronic State 301\n- -! 8-11. Atomic Term Symbols Are Used to Describe Atomic Spectra 302 Problems 308  \n- **@-1.** The Born-Oppenheimer Approximation Simplifies the Schrodinger Equation for Molecules 323\n- **9-2.** Hi Is the Prototypical Species of Molecular-Orbital Theory 325\n- 9-3. The Overlap Integral Is a Quantitative Measure of the Overlap of Atomic Orbitals Situated on Different Atoms 327\n- **9-4.** The Stability of a Chemical Bond Is a Quantum-Mechanical Effect 329\n- 9-5. The Simplest Molecular Orbital Treatment of Hi Yields a Bonding Orbital and an Antibonding Orbital 333\n- **9-6.** A Simple Molecular-Orbital Treatment of H2 Places Both Electrons in a Bonding Orbital 336\n- 9-7. Molecular Orbitals Can Be Ordered According to Their Energies 336\n- **9-8.** Molecular-Orbital Theory Predicts That a Stable Diatomic Helium Molecule Does Not Exist 341\n- **9-9.** Electrons Are Placed into Molecular Orbitals in Accord with the Pauli Exclusion Principle 342\n- **9-10.** Molecular-Orbital Theory Correctly Predicts That Oxygen Molecules Are Paramagnetic 344\n- **9-11.** Photoelectron Spectra Support the Existence of Molecular Orbitals 346\n- **9-12.** Molecular-Orbital Theory Also Applies to Heteronuclear Diatomic Molecules 346\n- **9-13.** An SCF-LCAO-MO Wave Function Is a Molecular Orbital Formed from a Linear Combination of Atomic Orbitals and Whose Coefficients Are Determined Self-Consistently 349\n- **9-14.** Electronic States of Molecules Are Designated by Molecular Term Symbols 355\n- **9-15.** Molecular Term Symbols Designate the Symmetry Properties of Molecular Wave Functions 358\n- **9-16.** Most Molecules Have Excited Electronic States 360",
+    "metadata": {
+      "Header 1": "**CHAPTER 1** I The Dawn of the Quantum Theory",
+      "Header 2": "Introduction to Complex Numbers",
+      "is_merged_section": true,
+      "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/F814BC5915875384820.pdf"
+    }
+  },
+  {
+    "page_content": "- 1-1. Blackbody Radiation Could Not Be Explained by Classical Physics 2\n- 1-2. Planck Used a Quantum Hypothesis to Derive the Blackbody Radiation Law 4\n- 1-3. Einstein Explained the Photoelectric Effect with a Quantum Hypothesis 7\n- 1-4. The Hydrogen Atomic Spectrum Consists of Several Series of Lines 10\n- 1-5. The Rydberg Formula Accounts for All the Lines in the Hydrogen Atomic Spectrum 13\n- 1-6. Louis de Broglie Postulated That Matter Has Wavelike Properties 15\n- 1-7. de Broglie Waves Are Observed Experimentally 16\n- 1-8. The Bohr Theory of the Hydrogen Atom Can Be Used to Derive the Rydberg Formula 18\n- 1-9. The Heisenberg Uncertainty Principle States That the Position and the Momentum of a Particle Cannot Be Specified Simultaneously with Unlimited Precision 23  \nProblems 25\n\nProblems 35",
+    "metadata": {
+      "Header 1": "Chapter 8",
+      "Header 2": "Introduction to Probability",
+      "is_merged_section": true,
+      "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/F814BC5915875384820.pdf"
+    }
+  },
+  {
+    "page_content": "- 2-1. The One-Dimensional Wave Equation Describes the Motion of a Vibrating String 39\n- 2-2. The Wave Equation Can Be Solved by the Method of Separation of Variables 40\n- 2-3. Some Differential Equations Have Oscillatory Solutions 44\n- 2-4. The General Solution to the Wave Equation Is a Superposition of Normal Modes 46\n- 2-5. A Vibrating Membrane Is Described by a Two-Dimensional Wave Equation 49  \nProblems 54\n\nProblems 70",
+    "metadata": {
+      "Header 1": "Chapter 8",
+      "Header 2": "Basic Concepts of Statistics",
+      "is_merged_section": true,
+      "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/F814BC5915875384820.pdf"
+    }
+  },
+  {
+    "page_content": "- **3-1.** The Schrödinger Equation Is the Equation for Finding the Wave Function of a Particle 73\n- **3-2.** Classical-Mechanical Quantities Are Represented by Linear Operators in Ouantum Mechanics 75\n- 3-3. The Schrödinger Equation Can Be Formulated As an Eigenvalue Problem 77\n- **3-4.** Wave Function's Have a Probabilistic Interpretation 80\n- **3-5.** The Energy of a Particle in a Box Is Quantized 81\n- 3-6. Wave Functions Must Be Normalized 84\n- 3-7. The Average Momentum of a Particle in a Box Is Zero 86\n- **3-8.** The Uncertainty Principle Says That  $\\sigma_n \\sigma_r > \\hbar/2$  88\n- **3-9.** The Problem of a Particle in a Three-Dimensional Box Is a Simple Extension of the One-Dimensional Case 90  \nProblems 96  \n#### MATHCHAPTER C / Vectors 105  \nProblems 113\n\n- 4-1. The State of a System Is Completely Specified by Its Wave Function 115\n- 4-2. Quantum-Mechanical Operators Represent Classical-Mechanical Variables 118\n- **4-3.** Observable Quantities Must Be Eigenvalues of Quantum Mechanical Operators 122\n- **4-4.** The Time Dependence of Wave Functions Is Governed by the Time-Dependent Schrödinger Equation 125\n- **4-5.** The Eigenfunctions of Quantum Mechanical Operators Are Orthogonal 127\n- **4-6.** The Physical Quantities Corresponding to Operators That Commute Can Be Measured Simultaneously to Any Precision 131  \nProblems 134  \n![](_page_3_Picture_22.jpeg)",
+    "metadata": {
+      "Header 1": "Chapter 8",
+      "Header 2": "Descriptive Statistics",
+      "is_merged_section": true,
+      "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/F814BC5915875384820.pdf"
+    }
+  },
+  {
+    "page_content": "Problems 153\n\n- **5-1.** A Harmonic Oscillator Obeys Hooke's Law 157\n- **5-2.** The Equation for a Harmonic-Oscillator Model of a Diatomic Molecule Contains the Reduced Mass of the Molecule 161\n- **5-3.** The Harmonic-Oscillator Approximation Results from the Expansion of an Internuclear Potential Around Its Minimum 163\n- \\* 5-4. The Energy Levels of a Quantum-Mechanical Harmonic Oscillator Are  $E_v = \\hbar\\omega(v+\\frac{1}{2})$  with  $v=0,\\ 1,\\ 2,\\ \\dots$  166\n- 5-5. The Harmonic Oscillator Accounts for the Infrared Spectrum of a Diatomic Molecule 167\n- 5-6. The Harmonic-Oscillator Wave Functions Involve Hermite Polynomials 169\n- **5-7.** Hermite Polynomials Are Either Even or Odd Functions 172\n- **5-8** The Energy Levels of a Rigid Rotator Are  $E = \\hbar^2 J(J+1)/2I$  173  \n/~The Rigid Rotator Is a Model for a Rotating Diatomic Molecule 177 Problems 1 79",
+    "metadata": {
+      "Header 1": "Chapter 8",
+      "Header 2": "Probability Distributions",
+      "is_merged_section": true,
+      "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/F814BC5915875384820.pdf"
+    }
+  },
+  {
+    "page_content": "- 6-1. The Schrodinger Equation for the Hydrogen Atom Can Be Solved Exactly 191\n- 6-2. The Wave Functions of a Rigid Rotator Are Called Spherical Harmonics 193\n- 6-3. The Precise Values of the Three Components of Angular Momentum Cannot Be Measured Simultaneously 200\n- 6-4. Hydrogen Atomic Orbitals Depend upon Three Quantum Numbers 206\n- 6-5. *s* Orbitals Are Spherically Symmetric 209\n- 6-6. There Are Three *p*Orbitals for Each Value of the Principal Quantum Number, *<sup>n</sup>*~ 2 213\n- 6-7. The Schrodinger Equation for the Helium Atom Cannot Be Solved Exactly 219 Problems 220  \n#### MATHCHAPTER E I Determinants 231  \nProblems 238\n\n- <sup>~</sup>7-1. The Variational Method Provides an Upper Bound to the Ground-State Energy of a System 241\n- 7-2. A Trial Function That Depends Linearly on the Variational Parameters Leads to a Secular Determinant 249\n- 7-3. Trial Functions Can Be Linear Combinations of Functions That Also Contain Variational Parameters 256\n- <sup>~</sup>7-4. Perturbation Theory Expresses the Solution to One Problem in Terms of Another Problem Solved Previously 257  \nProblems 2 61  \n#### CHAPTER 8 I Multielectron Atoms 275  \n- 8-1. Atomic and Molecular Calculations Are Expressed in Atomic Units 275\n- 8-2. Both Perturbation Theory and the Variational Method Can Yield Excellent Results for Helium 278\n- 8-3. Hartree-Fock Equations Are Solved by the Self-Consistent Field Method 282\n- 8-4. An Electron Has an Intrinsic Spin Angular Momentum 284\n- 8-5. Wave Functions Must Be Antisymmetric in the Interchange of Any Two Electrons 285\n- 8-6. Antisymmetric Wave Functions Can Be Represented by Slater Determinants 288\n- 8-7. Hartree-Fock Calculations Give Good Agreement with Experimental Data 290\n- 8-8. A Term Symbol Gives a Detailed Description of an Electron Configuration 292\n- @jrhe Allowed Values of J are *L* + *S, L* + *S-* 1, 0 0 0, IL- Sl 296\n- 8-10. Hund's Rules Are Used to Determine the Term Symbol of the Ground Electronic State 301\n- -! 8-11. Atomic Term Symbols Are Used to Describe Atomic Spectra 302 Problems 308  \n- **@-1.** The Born-Oppenheimer Approximation Simplifies the Schrodinger Equation for Molecules 323\n- **9-2.** Hi Is the Prototypical Species of Molecular-Orbital Theory 325\n- 9-3. The Overlap Integral Is a Quantitative Measure of the Overlap of Atomic Orbitals Situated on Different Atoms 327\n- **9-4.** The Stability of a Chemical Bond Is a Quantum-Mechanical Effect 329\n- 9-5. The Simplest Molecular Orbital Treatment of Hi Yields a Bonding Orbital and an Antibonding Orbital 333\n- **9-6.** A Simple Molecular-Orbital Treatment of H2 Places Both Electrons in a Bonding Orbital 336\n- 9-7. Molecular Orbitals Can Be Ordered According to Their Energies 336\n- **9-8.** Molecular-Orbital Theory Predicts That a Stable Diatomic Helium Molecule Does Not Exist 341\n- **9-9.** Electrons Are Placed into Molecular Orbitals in Accord with the Pauli Exclusion Principle 342\n- **9-10.** Molecular-Orbital Theory Correctly Predicts That Oxygen Molecules Are Paramagnetic 344\n- **9-11.** Photoelectron Spectra Support the Existence of Molecular Orbitals 346\n- **9-12.** Molecular-Orbital Theory Also Applies to Heteronuclear Diatomic Molecules 346\n- **9-13.** An SCF-LCAO-MO Wave Function Is a Molecular Orbital Formed from a Linear Combination of Atomic Orbitals and Whose Coefficients Are Determined Self-Consistently 349\n- **9-14.** Electronic States of Molecules Are Designated by Molecular Term Symbols 355\n- **9-15.** Molecular Term Symbols Designate the Symmetry Properties of Molecular Wave Functions 358\n- **9-16.** Most Molecules Have Excited Electronic States 360",
+    "metadata": {
+      "Header 1": "Chapter 8",
+      "Header 2": "Inferential Statistics",
+      "is_merged_section": true,
+      "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/F814BC5915875384820.pdf"
+    }
+  },
+  {
+    "page_content": "- 4-1. The State of a System Is Completely Specified by Its Wave Function 115\n- 4-2. Quantum-Mechanical Operators Represent Classical-Mechanical Variables 118\n- **4-3.** Observable Quantities Must Be Eigenvalues of Quantum Mechanical Operators 122\n- **4-4.** The Time Dependence of Wave Functions Is Governed by the Time-Dependent Schrödinger Equation 125\n- **4-5.** The Eigenfunctions of Quantum Mechanical Operators Are Orthogonal 127\n- **4-6.** The Physical Quantities Corresponding to Operators That Commute Can Be Measured Simultaneously to Any Precision 131  \nProblems 134  \n![](_page_3_Picture_22.jpeg)",
+    "metadata": {
+      "Header 2": "**CHAPTER 4** / Some Postulates and General Principles of Quantum Mechanics 115",
+      "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/F814BC5915875384820.pdf"
+    }
+  },
+  {
+    "page_content": "Problems 153",
+    "metadata": {
+      "Header 2": "**CHAPTER 4** / Some Postulates and General Principles of Quantum Mechanics 115",
+      "Header 3": "MATHCHAPTER D / Spherical Coordinates 147",
+      "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/F814BC5915875384820.pdf"
+    }
+  },
+  {
+    "page_content": "- **5-1.** A Harmonic Oscillator Obeys Hooke's Law 157\n- **5-2.** The Equation for a Harmonic-Oscillator Model of a Diatomic Molecule Contains the Reduced Mass of the Molecule 161\n- **5-3.** The Harmonic-Oscillator Approximation Results from the Expansion of an Internuclear Potential Around Its Minimum 163\n- \\* 5-4. The Energy Levels of a Quantum-Mechanical Harmonic Oscillator Are  $E_v = \\hbar\\omega(v+\\frac{1}{2})$  with  $v=0,\\ 1,\\ 2,\\ \\dots$  166\n- 5-5. The Harmonic Oscillator Accounts for the Infrared Spectrum of a Diatomic Molecule 167\n- 5-6. The Harmonic-Oscillator Wave Functions Involve Hermite Polynomials 169\n- **5-7.** Hermite Polynomials Are Either Even or Odd Functions 172\n- **5-8** The Energy Levels of a Rigid Rotator Are  $E = \\hbar^2 J(J+1)/2I$  173  \n/~The Rigid Rotator Is a Model for a Rotating Diatomic Molecule 177 Problems 1 79",
+    "metadata": {
+      "Header 2": "CHAPTER 5 / The Harmonic Oscillator and the Rigid Rotator: Two Spectroscopic Models 157",
+      "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/F814BC5915875384820.pdf"
+    }
+  },
+  {
+    "page_content": "- 6-1. The Schrodinger Equation for the Hydrogen Atom Can Be Solved Exactly 191\n- 6-2. The Wave Functions of a Rigid Rotator Are Called Spherical Harmonics 193\n- 6-3. The Precise Values of the Three Components of Angular Momentum Cannot Be Measured Simultaneously 200\n- 6-4. Hydrogen Atomic Orbitals Depend upon Three Quantum Numbers 206\n- 6-5. *s* Orbitals Are Spherically Symmetric 209\n- 6-6. There Are Three *p*Orbitals for Each Value of the Principal Quantum Number, *<sup>n</sup>*~ 2 213\n- 6-7. The Schrodinger Equation for the Helium Atom Cannot Be Solved Exactly 219 Problems 220  \n#### MATHCHAPTER E I Determinants 231  \nProblems 238",
+    "metadata": {
+      "Header 2": "CHAPTER 5 / The Harmonic Oscillator and the Rigid Rotator: Two Spectroscopic Models 157",
+      "Header 3": "CHAPTER 6 I The Hydrogen Atom 191",
+      "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/F814BC5915875384820.pdf"
+    }
+  },
+  {
+    "page_content": "- <sup>~</sup>7-1. The Variational Method Provides an Upper Bound to the Ground-State Energy of a System 241\n- 7-2. A Trial Function That Depends Linearly on the Variational Parameters Leads to a Secular Determinant 249\n- 7-3. Trial Functions Can Be Linear Combinations of Functions That Also Contain Variational Parameters 256\n- <sup>~</sup>7-4. Perturbation Theory Expresses the Solution to One Problem in Terms of Another Problem Solved Previously 257  \nProblems 2 61  \n#### CHAPTER 8 I Multielectron Atoms 275  \n- 8-1. Atomic and Molecular Calculations Are Expressed in Atomic Units 275\n- 8-2. Both Perturbation Theory and the Variational Method Can Yield Excellent Results for Helium 278\n- 8-3. Hartree-Fock Equations Are Solved by the Self-Consistent Field Method 282\n- 8-4. An Electron Has an Intrinsic Spin Angular Momentum 284\n- 8-5. Wave Functions Must Be Antisymmetric in the Interchange of Any Two Electrons 285\n- 8-6. Antisymmetric Wave Functions Can Be Represented by Slater Determinants 288\n- 8-7. Hartree-Fock Calculations Give Good Agreement with Experimental Data 290\n- 8-8. A Term Symbol Gives a Detailed Description of an Electron Configuration 292\n- @jrhe Allowed Values of J are *L* + *S, L* + *S-* 1, 0 0 0, IL- Sl 296\n- 8-10. Hund's Rules Are Used to Determine the Term Symbol of the Ground Electronic State 301\n- -! 8-11. Atomic Term Symbols Are Used to Describe Atomic Spectra 302 Problems 308  \n- **@-1.** The Born-Oppenheimer Approximation Simplifies the Schrodinger Equation for Molecules 323\n- **9-2.** Hi Is the Prototypical Species of Molecular-Orbital Theory 325\n- 9-3. The Overlap Integral Is a Quantitative Measure of the Overlap of Atomic Orbitals Situated on Different Atoms 327\n- **9-4.** The Stability of a Chemical Bond Is a Quantum-Mechanical Effect 329\n- 9-5. The Simplest Molecular Orbital Treatment of Hi Yields a Bonding Orbital and an Antibonding Orbital 333\n- **9-6.** A Simple Molecular-Orbital Treatment of H2 Places Both Electrons in a Bonding Orbital 336\n- 9-7. Molecular Orbitals Can Be Ordered According to Their Energies 336\n- **9-8.** Molecular-Orbital Theory Predicts That a Stable Diatomic Helium Molecule Does Not Exist 341\n- **9-9.** Electrons Are Placed into Molecular Orbitals in Accord with the Pauli Exclusion Principle 342\n- **9-10.** Molecular-Orbital Theory Correctly Predicts That Oxygen Molecules Are Paramagnetic 344\n- **9-11.** Photoelectron Spectra Support the Existence of Molecular Orbitals 346\n- **9-12.** Molecular-Orbital Theory Also Applies to Heteronuclear Diatomic Molecules 346\n- **9-13.** An SCF-LCAO-MO Wave Function Is a Molecular Orbital Formed from a Linear Combination of Atomic Orbitals and Whose Coefficients Are Determined Self-Consistently 349\n- **9-14.** Electronic States of Molecules Are Designated by Molecular Term Symbols 355\n- **9-15.** Molecular Term Symbols Designate the Symmetry Properties of Molecular Wave Functions 358\n- **9-16.** Most Molecules Have Excited Electronic States 360",
+    "metadata": {
+      "Header 2": "CHAPTER 5 / The Harmonic Oscillator and the Rigid Rotator: Two Spectroscopic Models 157",
+      "Header 3": "CHAPTER 7 I Approximation Methods 241",
+      "source_pdf": "/share/project/bs_scaling/lmse/self-evolution-explore/datasets/websources/Chemistry/F814BC5915875384820.pdf"
+    }
+  }
+]

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