Unit 1: 2D & 3D Wave Mech.

Question 1

Momentum and Energy Relation:
- Momentum equation string
- Energy equation string

Answer 1

Question 2

Kinetic Energy:
(“Non-operator” version)

Answer 2

Question 3

Wave Function Constraints

Answer 3

Question 4

STM Imaging Condition:

Answer 4

Question 5

What is the modulus square of a complex exponential:

Answer 5

Question 6

3D Potential and Wave Function Separation:

Answer 6

Question 7

3D Schrödinger Equation:

Answer 7

Question 8

Separated Schrödinger Equation for Each Dimensions:

Answer 8

Question 9

Total Energy in 3D:

Answer 9

Question 10

Energy Levels in a 3D Box:
(In terms of box length)

Answer 10

Question 11

Wave Function in a 3D Box:

Answer 11

Question 12

Wave function in a 3D Box with Trigonometric Terms:

Answer 12

Question 13

Harmonic Oscillator Potential Equation with Solutions:
(1D)
(Can include graph)

Answer 13

Question 14

Energy levels of Harmonic Oscillator:

Answer 14

Question 15

Wave Functions in Spherical Coordinates:
(Separated)

Answer 15

Question 16

Probability Density in Spherical Coordinates:
- between 2 values of r

Answer 16

Question 17

Radial Probability Density:

Answer 17

Question 18

Average Radius:

Answer 18

Question 19

Separation of Solutions in Polar Coordinations:
(Separation of Sch. =n in Spherical Polar Co-ords)
(3 separate equations)

Answer 19

Question 20

Magnetic Quantum Number:

Answer 20

Question 21

Hydrogenic Atom Potential:

Answer 21

Question 22

Energy Levels of Hydrogenic Atom:

Answer 22

Question 23

Energy in an Infinite Square Potential Well:

Answer 23

Question 24

Wave functions in an Infinite Potential Well:
(The 2 usual cases)

Answer 24

Question 25

Expectation Value of Position:
(General)

Answer 25

Question 26

Heisenberg Uncertainty Principle:

Answer 26

Question 27

Kinetic Energy in Quantum Mechanics:
(3 equation string)

Answer 27

Question 28

Translation of the Well:
(Definition)

Answer 28

Question 29

Degeneracy of States:
(Definition with diagram)
- How are states degenerate?

Answer 29

Question 30

Degree of Degeneracy:
(Definition)

Answer 30

Question 31

Sketch of the ground state probability density: infinite well & harmonic oscillator

Answer 31

Question 32

Potential of a 3D Harmonic Oscillator:
(String equation, 2 components)

Answer 32

Question 33

Energy Levels of a 3D Isotropic Harmonic Oscillator:

Answer 33

Question 34

Probability Distribution in 3D Isotropic Harmonic Oscillator:
(Average probability over all degenerate states of: u_110, u_200)

Answer 34

Question 35

Energy Levels of a 2D Non-Isotropic Harmonic Oscillator:

Answer 35

Question 36

Energy Levels of a 2D Isotropic Harmonic Oscillator with Equal Frequencies:

Answer 36

Question 37

Normalisation of the Wave Function in Spherical Coordinates:

Answer 37

Question 38

Radial and Angular Normalisation Conditions:

Answer 38

Question 39

Spherical Harmonics:

Answer 39

Question 40

Angular Momentum Quantisation:
- Modulus squared
- Arbitrary Z axis

Answer 40

Question 41

Potential Energy in a Hydrogenic Atom:

Answer 41

Question 42

Classical Turning Point for Harmonic Oscillator:
- statement
- energy at pt

Answer 42