A particle in a finite potential well has energy E, as shown below. The wave function in region II where x 0 has the form $\Psi$II =
A)Ae-Cx.
B)AeCx.
C)F sin kx.
D)G cos kx.
E)F sin kx + G cos kx.

Question

A particle in a finite potential well has energy E, as shown below.  The wave function in region II where x > 0 has the form $\Psi$II =
A)Ae-Cx. 
B)AeCx. 
C)F sin kx. 
D)G cos kx. 
E)F sin kx + G cos kx.

Quizplus · Accepted Answer

Since the particle is in a finite potential well, the energy is quantized and only certain values are allowed. Therefore, we can assume that the particle is in a bound state and the wave function must be a combination of sine and cosine functions. Additionally, since the potential is symmetrical about x = 0, the wave function must also be symmetrical about x = 0. Thus, the best choice is E, which is a combination of sine and cosine functions.

A Particle in a Finite Potential Well Has Energy E Ψ\PsiΨ

A Particle in a Finite Potential Well Has Energy E $\Psi$