1000 Solved Problems in Modern Physics

Appendix: Problem Index 609

(a)σyis real (b) Eigen value and Eigen vectors (c) projector

operators

2.79

(i)σx^2 =1 (ii) [σx,σy]= 2 iσz 2.80

Condition for two operators to commute 2.81

2.2.8 Uncertainty Principle

Ground state energy of a linear oscillator 2.82

Uncertainty for energy and momentum 2.83

Uncertainty for position and momentum 2.84

KE of electron in H-atom 2.85

Two uncertainty principles, KE of neutron in nucleus. 2.86

Chapter 3 Quantum Mechanics 2

3.2.1 Wave Function

Infinitely deep potential well-photon energy 3.1

Variance of Gaussian function 3.2

Normalization constant 3.3

Flux of particles 3.4

Klein–Gordon equation-probability density 3.5

Normalized wave functions for square well 3.6

Thomas-Reich-Kuhn sum rule 3.7

Laporte rule 3.8

Eigen values of a hermitian operator 3.9

Rectangular distribution ofψ, Normalization constant, Constant

probability,<x>,σ^2 , momentum probability distribution

3.10, 11

Probability for exponentialψ 3.12

3.2.2 Schrodinger Equation
Solution of radial equation forn= 23 .13
Ehrenfest’s theorem 3.14
Separation of equation intor,θand ø parts 3.15
Derivation of quantum numberm 3.16
Derivation of quantum numberl 3.17

3.2.3 Potential Wells and Barriers

Particle trapped in potential well of infinite depth. Wave functions

and Eigen values

3.18, 48

V 0 R^2 =constant for deuteron 3.19

Expectation value of potential energy of deuteron 3.20

Average distance of separation and interaction ofnandPin

deuteron

3.21

V 0 for deuteron 3.22, 29

Root mean square separation ofn&pin deuteron 3.23

Photon wavelength for transition of electron trapped in a potential

well

3.24