Question

1. Suppose we didn't actually know the wave functions for a particle in a box. Reasonable guesses for the ground- and first-excited-state wave functions might be functions of the form 1 = a y (1 - y) 02 = by (y-c)(y-1), where y = (x/L), L is the length of the box, and a, b, and care constants. (a) These functions have quite a number of features that make them sensible guesses. Sketch both functions and list these special features. (b) These two functions must be orthogonal in the interval 0 SX SL to be wave functions. Use this fact to find the constant c. Why might you have known the value of c from symmetry considerations alone? (c) The functions must also be normalized, of course. Find the constants a and b.

Answer 1

The answer is in 4 sheets.

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