Question

Consider the wave function

Ψ = Ae^−α|x|

Which of the following boundary conditions are satisfied by the wave function?

Group of answer choices

Ψ approaches zero as x approaches ±∞

Ψ is single valued.

Ψ is finite everywhere.

None of the boundary conditions are satisfied.

Answer 1

For a acceptable wave function the following conditions must be satisfied.

1. The wave function ψ must be continuous. And all its partial derivatives must also be continuous

2. The wave function ψ must be quadratically integrable.

That is there must exist

3. The wave function must be single valued , since is the probability density.

4. The wave function should be finite everywhere.

Here the wave function is,

For the value wave function becomes,

,

(since )

So, first condition is satisfied.

The wave function cannot take two values at a time so, it is single valued

Therefore the wave function satisfies the second condition.

And for every values of x the wave function give a finite value. so, the wave function also satisfies the third condition.