1000 Solved Problems in Modern Physics

610 Appendix: Problem Index

Class I and II solutions of Eigen values for particle in a potential

well of finite depth.

3.25

Fraction of time that neutron and proton in deuteron are outside

range of nuclear forces

3.26

Results of energy levels for infinite well follow from finite well 3.27

Impossibility of excited states of deuteron 3.28

Transmission of particles through potential barrier 3.30, 31

Expected energy value for particle in a harmonic potential well 3.32

Infinitely deep potential well, momentum distribution 3.33

Quantum mechanical tunneling of alpha particle 3.34

One dimensional potential well, condition for one bound state and

two bound states

3.35

To express normalization constant A in terms ofα,βand a in

Problem 3.25

3.36

Mean position and variance for particle in an infinitely deep well 3.37

Energy eigen values for given Hamiltonian 3.38

Eigen value for 3-D rectangular well 3.39

Degeneracy of energy levels in (3.39) 3.40

Potential step 3.41, 42

A 1-D potential well hasψ(x)=Acos

( 3 πx

L

)

for−L/ 2 ≤x≤L/ 2

and zero elsewhere. To find probability and Eigen value

3.43

“Top hat” potential; transmission coefficient. Numerical problem 3.44

Energy eigen functions and eigen values for 2D potential well 3.45

Number of states with energy less thanEin 3-D infinite

potential well

3.46

Force exerted on the walls of a hollow sphere by a particle 3.47

Transmission amplitude of a beam of particles through

a rectangular well

3.49

Real and virtual particles. Klein–Gordon equation

and Yukawa’s potential

3.50

3.2.4 Simple Harmonic Oscillator (SHO)

Hermite equation for SHO 3.51

Probability in classical forbidden region 3.52

Energy of a 3-D SHO 3.53

Zero point energy and uncertainty principle 3.54

Forn→∞,Q.M.SHO→classical SHO 3.55

Probability distribution for classical SHO 3.56

EandV(x)for potential well,ψ∼exp(−x^2 / 2 a^2 )3.57

SHO and uncertainty principle 3.58

Vibrational or rotational transitions from a set of wave numbers 3.59

Degeneracy of energy levels of isotropic oscillator 3.60

Oscillations of probability density of SHO state 3.61

Given the eigen functions of SHO, to find the expectation

value of energy

3.62

Eigen functions and eigen values for the lowest two states 3.63