Solution Manual for Quantum Mechanics

Ahmed Ishtiaq, Fayyazuddin, Riazuddin

• Publisher: WSPC
• Year: 2014
• ISBN:
  9789814541909
• Topic: Naturwissenschaften
• Subtopic: Atom- & Molekularphysik

This is the solution manual for Riazuddin's and Fayyazuddin's Quantum Mechanics (2nd edition). The questions in the original book were selected with a view to illustrate the physical concepts and use of mathematical techniques which show their universality in tackling various problems of different physical origins. This solution manual contains the text and complete solution of every problem in the original book. This book will be a useful reference for students looking to master the concepts introduced in Quantum Mechanics (2nd edition). Contents:

• Breakdown of Classical Concepts
• Quantum Mechanical Concepts
• Basic Postulates of Quantum Mechanics
• Solution of Problems in Quantum Mechanics
• Simple Harmonic Oscillator
• Angular Momentum
• Motion in Centrally Symmetric Field
• Collision Theory
• Operators
• Heisenberg Equation of Motion, Invariance Principle and Path Integral
• Angular Momentum and Spin
• Time Independent Perturbation Theory
• Time Dependent Perturbation Theory
• Statistics and the Exclusion Principle
• Two State Systems
• Quantum Computation
• Perturbation Induced by Electromagnetic Field
• Formal Theory of Scattering
• S-Matrix and Invariance Principles
• Relativistic Quantum Mechanics: Dirac Equation
• Dirac Equation in (1+2) Dimensions: Application to Graphene

Readership: Students and teachers of quantum mechanics. Key Features:

• It's a solution manual
• Pretty self-explanatory

Chapter 1

Breakdown of Classical Concepts

The following formulae are relevant for the solution of the problems in this chapter.

For photons

For particles

ħ = 6.582 × 10⁻²² MeV.s, cħ = 1.97 × 10⁻¹³ MeV.m, c ≈ 3 × 10⁸ m.s⁻¹

Q1.1 Find the energy and momentum of an X-ray photon whose frequency is 5 × 10¹⁸ cycles sec⁻¹.

Solution:

Q1.2 (a) The velocity of ripples on a liquid surface is

where S is the surface tension and ρ the density of the liquid. Find the group velocity of these waves.

(b) Velocity of ocean waves is

where g is the acceleration due to gravity. Find the group velocity of ocean waves.

Solution: (a)

and

v = νλ

Thus

Now

(b) For the ocean wave

we get

Q1.3 Given that

Find

. Make a sketch of A(k) and

and hence show that ΔkΔx > 1.

Solution: To find

use Eq. (1.1b) from the book,

A sketch of A(k) and

are shown in Figs. 1.1 and 1.2 respectively. It is clear from these figures that Δk = 2K and

so that ΔkΔx = 2π > 1, in conformity with the well known relation ΔxΔk ≥ 1 of wave optics.

Fig. 1.1Sketch of A(k).

Fig. 1.2Sketch of

.

Q1.4 For a Guassian wave packet

Show that...