Question

The wave function given below is suggested to fit the particle in a box of length L in one dimension: Duh!! also known as the particle on a line: V=N (L x-); where N is the normalization constant. Problem One. List three conditions (in a short phrase) that make any wavefunction acceptable. For each condition, show that the above wavefunction satisfies the condition you listed. (Use the allotted spaces below to answer the question). (1) (III).

Answer 1

Conditions of acceptable wave functions:

1. Wave function $\psi$ , must be finite for finite value of x.

Here, , is finite for any finite values of x. ( As, both N and L are constants).

(227)N =

2. Wave function $\psi$ , must be singled valued for a fixed value of x.

Here , is singled valued for any fixed value of x. ( As here N and L are independent of x).

(227)N =

3. Wave function must be normalized.

Here is normalized, where N is normalization constant.

(227)N =