SKEDSOFT

Introduction:

Time-independent form of the Schrödinger wave equation in one-dimension.

Explanation of Eigen value particles in a potential well of infinite depth:

The time-independent form of the Schrödinger wave equation in one-dimension is given by,

Consider a particle trapped in a potential well of infinite depth and width L. A particle in this potential is completely free i.e., potential energy is zero, except at the two ends (x = 0 and x = L), where an infinite force prevents it from escaping;

But within the well the particle does not lose any energy when it collides with the walls and hence the total energy of the particle remains constant. Since the article cannot exist outside the box, we have

The Schrödinger equation for such case takes the form

where E is the total energy of the particle and is purely in the form of kinetic energy. The general solution of such a differential equation is of the form

We use the boundary conditions to find out the constants A and B. Applying the condition

Now, we use the second boundary condition