# Physics 2130 Foundations of Modern Physics Quantum Mechanics

• Slides: 58

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 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 75 Physics 2130, Spring 2019

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 77 Physics 2130, Spring 2019

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

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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 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, ny=3 Clicker Slide 86 Physics 2130, Spring 2019

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 E) 5 Clicker Slide 88 Physics 2130, Spring 2019

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) 3 D) 4 E) 5 Clicker Slide 90 Physics 2130, Spring 2019

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z Clicker Slide 101 Physics 2130, Spring 2019

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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 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 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 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 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 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 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 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 E) purple F) yellow-green Physics 2130, Spring 2019

Physics 2130, Spring 2019

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

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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 115 Physics 2130, Spring 2019

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 Physics 2130, Spring 2019

Stable atomic nuclei with spin>0

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 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