Rapidshare problems and solutions on quantum mechanics

Account Options Sign in. Try the new Google Books. Check out the new look and enjoy easier access to your favorite features. Try it now. No thanks. PHI Learning Pvt. Quantum mechanics is an important area of physics and students of ten find it 'tough' from the understanding point of view.

By providing problems with their solutions, Professor Aruldhas, with his expertise in and long experience of teaching the subject, makes the students comprehend the fundamental concepts of Quantum Mechanics with ease. Kyriakos Tamvakis studied at the University of Athens and gained his Ph. Professor Tamvakis has published 90 articles on theoretical high-energy physics in various journals and has written two textbooks in Greek, on quantum mechan- ics and on classical electrodynamics.

Tamvakis Information on this title: www. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. It is addressed to both student and teacher and is intended to be used as an auxiliary tool in class or in self- study. The emphasis is on stressing the principles, physical concepts and methods rather than supplying information for immediate use.

The problems have been designed primarily for their educational value but they are also used to point out certain properties and concepts worthy of interest; an additional aim is to condition the student to the atmosphere of change that will be encountered in the course of a career. Later, Kronig and Penney extended this idea to explain the motion of a charge carrier in a periodic potential which is nothing but the one-dimensional lattices.

The Dirac delta potential is infinitesimally narrow potential only at some point generally at the origin, for convenience [ 3 ]. The potential of the system.

Dirac delta potential. So the coefficients A 1 and A 2 are equal. The first derivatives are related by the following equation. The energy eigen value expression does not have any integer like in the case of the potential well.

The eigen function can be evaluated as follows: The eigen function is always continuous. Hence the eigen function is. Simple harmonic oscillator, damped harmonic oscillator, and force harmonic oscillator are the few famous problems in classical physics.

But if one looks into the atomic world, the atoms are vibrating even at 0 K. Such atomic oscillations need the tool of quantum physics to understand its nature. In all the previous examples, the potential is constant in any particular region. Potential energy of the linear harmonic oscillator. Based on the asymptotic solution, the general solution of Eq. The solution given in Eq.

This gives the energy eigen value as. This minimum energy is known as ground state energy. Hence the energy difference between any two successive levels is constant. But this is not true in the case of real oscillators. The operator method is also one of the convenient methods to solve the exactly solvable problem as well as approximation methods in quantum mechanics [ 5 ]. The Hamiltonian of the linear harmonic oscillator is given as,. Here, x p represents the commutation between the operators x and p.

Adding Eqs. Subtracting Eq. This can be simplified as. Hence, one can generalize the result as. In order to evaluate the uncertainties x 2 , x 2 , p 2 , and p 2 have to be evaluated. The expectation value of the position in any state is zero. The expectation value of momentum is. Not only position, the expectation value of momentum in any state is also zero.

From Eq. The minimum uncertainty state is the ground state.