ABSTRACT
This chapter exclusively deals with the application of Schrödinger equation on various systems such as the particle in a box; the particle in a rectangular three-dimensional box; energy levels for a cubic potential box; the tunnel effect; the final equation for tunnel effect, that is, transparency factor which gives a clue to understand that the probability of transmission decreases rapidly as the width of the barrier increases; quantum mechanical explanation of emission of α-particle; the particle on a ring considering spherical polar co-ordinates; and the particle on sphere.
This chapter also comprises the Legendre polynomials, associated Legendre equation, associated Legendre function and spherical harmonics, Hermite polynomials and its applications, and orthogonal properties of Hermite polynomials.
It also provides the standard topics like simple linear harmonic oscillator, and its classical and quantum mechanical treatment which also includes the asymptotic and series solutions and energy levels of a linear harmonic oscillator.
The Schrödinger equation also plays with rigid rotors comprising its rigorous treatment and also the F and T equations which are very important.
The chapter ends with the references, standard several computational problems, questions on concepts, and also standard numerical problems for the benefits of the readers.
