Quantum Mechanics, Particle in a box

An attractive, one-dimensional square well has depth V₀ as shown above. Which of the following best shows a possible wave function for a bound state?

(GR9277 #29)

Solution:

1-D square well with depth  V₀  → finite potential well.

Wave function of a particle in finite potential well should have these following properties:

• ψ →0 as x → ± ∞ or get further into regions where the classical particle cannot penetrate at all due to its inadequate energy
• ψ is always a decaying exponential function
• ψ must be continuous and differentiable

Therefore:

A. FALSE. ψ does not go to zero as x → ±∞

C. FALSE. ψ is not continuous

D and E are FALSE. ψ are not decaying exponential functions

Answer: B