S. Lokanathan

Effects of Magnetic Field

Studies on the interaction of magnetic field with particles are of immense importance in many diverse areas. For example, in spectroscopy, the splitting of lines in a magnetic field (which leads to Zeeman and Paschen-Back effects, see Problems 20.1–20.4) is a subject of considerable importance (see, e.g. Ref. 1). In solid state physics, the calculation of diamagnetic and paramagnetic susceptibilities (see Problem 20.11) and the experiments on electron spin resonance and nuclear magnetic resonance (see Chapter 14), have immense practical importance (see, e.g. Ref 2–5).

The Dirac Delta Function

The Dirac delta function is used so extensively in quantum mechanics that we felt we should discuss it right in the beginning of the book, rather than relegating it to an appendix!

Bound State Solutions of the Schrödinger Equation

When the Hamiltonian for a system is independent of time, there is an essential simplification in that the general solution of the Schrodinger equation can be expressed as a function of spatial coordinates and a function of time. Thus, assuming the potential energy function to be independent of time, the one-dimensional time dependent Schrodinger equation [see Eq. (25) of Chapter 4] is given by

Time Dependent Perturbation Theory

i\frac{{\partial \psi }}{{\partial \mu }} = - \frac{{{^2}}}{{2\mu }}\,\frac{{{\partial ^2}\psi }}{{\partial {x^2}}} + V\left( x \right)\;\psi \left( {x,t} \right)

Linear Harmonic Oscillator: I Solution of the Schrödinger Equation and Relationship with the Classical Oscillator

(1) where μ represents the mass of the particle. The above equation can be solved by using the method of separation of variables

Experiments with Spin Half Particles The Stern-Gerlach Experiment, Larmor Precession and Magnetic Resonance

\psi \left( {x,t} \right) = \psi \left( x \right)\;T\;\left( t \right)