Physics 2130 Foundations of Modern Physics Quantum Mechanics

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Physics 2130 Foundations of Modern Physics Quantum Mechanics Part III: The Schrödinger Equation in

Physics 2130 Foundations of Modern Physics Quantum Mechanics Part III: The Schrödinger Equation in Two and Three Dimensions Clicker Questions Lecture Slides Professor John Price, Spring 2019

The Schrödinger Equation in 2 D and 3 D TZD Chapter 8 Schrödinger equation

The Schrödinger Equation in 2 D and 3 D TZD Chapter 8 Schrödinger equation in 2 D and 3 D Particle in a 2 D box 2 D central force problem 3 D central force problem Hydrogen atom Electron Spin (TZD 9. 1, 9. 2) Many Particles (TZD 10. 1 – 10. 5) 2

Plane waves in 2 dimensions y x A) B) C) D) E) Clicker Slide

Plane waves in 2 dimensions y x A) B) C) D) E) Clicker Slide 75 Physics 2130, Spring 2019

Plane waves in 2 dimensions y x A) B) C) D) E) Clicker Slide

Plane waves in 2 dimensions y x A) B) C) D) E) Clicker Slide 76 Physics 2130, Spring 2019

Plane waves in 2 dimensions y x A) B) C) D) E) Clicker Slide

Plane waves in 2 dimensions y x A) B) C) D) E) Clicker Slide 77 Physics 2130, Spring 2019

Plane waves in 2 dimensions y x A) B) C) D) E) Clicker Slide

Plane waves in 2 dimensions y x A) B) C) D) E) Clicker Slide 78 Physics 2130, Spring 2019

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Clicker Slide 79 Physics 2130, Spring 2019

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Clicker Slide 81 Physics 2130, Spring 2019

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Clicker Slide 83 Physics 2130, Spring 2019

y a 0 Clicker Slide 84 Physics 2130, Spring 2019 0 a x

y a 0 Clicker Slide 84 Physics 2130, Spring 2019 0 a x

What is this? A) A stationary-state probability density of the 2 D square well

What is this? A) A stationary-state probability density of the 2 D square well B) The real part of a stationary-state wavefunction of the 2 D square well C) The real part of a time-dependent wavefunction of the 2 D square well at t=0. D) B or C E) None of the above Clicker Slide 85 Physics 2130, Spring 2019

What is this? A) nx=3, ny=3 B) nx=4, ny=4 C) nx=3, ny=4 D) nx=4,

What is this? A) nx=3, ny=3 B) nx=4, ny=4 C) nx=3, ny=4 D) nx=4, ny=3 Clicker Slide 86 Physics 2130, Spring 2019

The energy of this state is…. multiplied by A) 9 B) 16 C) 18

The energy of this state is…. multiplied by A) 9 B) 16 C) 18 D) 24 E) 32 Clicker Slide 87 Physics 2130, Spring 2019

The degeneracy of this level is…. A) 1 B) 2 C) 3 D) 4

The degeneracy of this level is…. A) 1 B) 2 C) 3 D) 4 E) 5 Clicker Slide 88 Physics 2130, Spring 2019

ny The degeneracy of this level is…. A) 1 B) 2 nx C) 3

ny The degeneracy of this level is…. A) 1 B) 2 nx C) 3 D) 4 E) 5 Clicker Slide 89 Physics 2130, Spring 2019

The degeneracy of the level with nx=1, ny=3 is… A) 1 B) 2 C)

The degeneracy of the level with nx=1, ny=3 is… A) 1 B) 2 C) 3 D) 4 E) 5 Clicker Slide 90 Physics 2130, Spring 2019

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Clicker Slide 91 Physics 2130, Spring 2019

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Clicker Slide 92 Physics 2130, Spring 2019

Clicker Slide 92 Physics 2130, Spring 2019

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Clicker Slide 95 Physics 2130, Spring 2019

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Clicker Slide 96 Physics 2130, Spring 2019

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Clicker Slide 97 Physics 2130, Spring 2019

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Clicker Slide 98 Physics 2130, Spring 2019

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Clicker Slide 99 Physics 2130, Spring 2019

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Clicker Slide 100 Physics 2130, Spring 2019

 z Clicker Slide 101 Physics 2130, Spring 2019

z Clicker Slide 101 Physics 2130, Spring 2019

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Clicker Slide 105 Physics 2130, Spring 2019

These are plots of R(r). Which one is n=1, l=0? A) blue B) dark

These are plots of R(r). Which one is n=1, l=0? A) blue B) dark green C) red D) blue-green E) purple F) yellow-green Clicker Slide 106 Physics 2130, Spring 2019

These are plots of R(r). Which one is n=1, l=0? A) blue B) dark

These are plots of R(r). Which one is n=1, l=0? A) blue B) dark green C) red D) blue-green E) purple F) yellow-green Clicker Slide 106 Physics 2130, Spring 2019

These are plots of R(r). Which one is n=2, l=1? A) blue B) dark

These are plots of R(r). Which one is n=2, l=1? A) blue B) dark green C) red D) blue-green E) purple F) yellow-green Clicker Slide 107 Physics 2130, Spring 2019

These are plots of R(r). Which one is n=2, l=1? A) blue B) dark

These are plots of R(r). Which one is n=2, l=1? A) blue B) dark green C) red D) blue-green E) purple F) yellow-green Clicker Slide 107 Physics 2130, Spring 2019

These are plots of R(r). Which one is n=3, l=2? A) blue B) dark

These are plots of R(r). Which one is n=3, l=2? A) blue B) dark green C) red D) blue-green E) purple F) yellow-green Clicker Slide 108 Physics 2130, Spring 2019

These are plots of R(r). Which one is n=3, l=2? A) blue B) dark

These are plots of R(r). Which one is n=3, l=2? A) blue B) dark green C) red D) blue-green E) purple F) yellow-green Clicker Slide 108 Physics 2130, Spring 2019

These are plots of R(r). Which one is n=2, l=0? A) blue B) dark

These are plots of R(r). Which one is n=2, l=0? A) blue B) dark green C) red D) blue-green E) purple F) yellow-green Clicker Slide 109 Physics 2130, Spring 2019

These are plots of R(r). Which one is n=2, l=0? A) blue B) dark

These are plots of R(r). Which one is n=2, l=0? A) blue B) dark green C) red D) blue-green E) purple F) yellow-green Clicker Slide 109 Physics 2130, Spring 2019

These are plots of R(r). A) blue B) dark green C) red D) blue-green

These are plots of R(r). A) blue B) dark green C) red D) blue-green E) purple F) yellow-green Physics 2130, Spring 2019

Physics 2130, Spring 2019

Physics 2130, Spring 2019

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Clicker Slide 110 Physics 2130, Spring 2019

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Clicker Slide 111 Physics 2130, Spring 2019

Radial “shells”

Radial “shells”

2 p states (n=2, l=1) m=0 m=± 1 states

2 p states (n=2, l=1) m=0 m=± 1 states

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Clicker Slide 112 Physics 2130, Spring 2019

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Clicker Slide 113 Physics 2130, Spring 2019

 Can we solve this in the form A) YES B) NO C) What

Can we solve this in the form A) YES B) NO C) What do you mean, we? Clicker Slide 114 Physics 2130, Spring 2019

 Can we solve this in the form A) YES B) NO Clicker Slide

Can we solve this in the form A) YES B) NO Clicker Slide 115 Physics 2130, Spring 2019

 Can we solve this in the form A) YES B) NO Clicker Slide

Can we solve this in the form A) YES B) NO Clicker Slide 116 Physics 2130, Spring 2019

 Is this the TISE for helium? A) YES B) NO Clicker Slide 117

Is this the TISE for helium? A) YES B) NO Clicker Slide 117 Physics 2130, Spring 2019

Stable atomic nuclei with spin>0

Stable atomic nuclei with spin>0

If the three wavefunctions a, b, and c are all different, is this a

If the three wavefunctions a, b, and c are all different, is this a correct product state for three non-interacting electrons? A) Yes B) No Clicker Slide 118 Physics 2130, Spring 2019

If the three wavefunctions a, b, and c are all different, is this a

If the three wavefunctions a, b, and c are all different, is this a correct product state for three non-interacting electrons? A) Yes B) No Clicker Slide 119 Physics 2130, Spring 2019

Antisymmetric product states can also be written as determinants: Physics 2130, Spring 2019

Antisymmetric product states can also be written as determinants: Physics 2130, Spring 2019