Which of the following is not necessary as a boundary condition ...

[meagbuch]

Which of the following is not necessary as a boundary condition for a wave function?
 
 

a. The wave function must approach a finite number or zero over any limit.
  b. The wave function must be a function for each of the dimensions it depends on (single-valued for each variable independently).

 

c. The wave function must approach zero when x
  d. The wave function must approach zero as x L, where L is a boundary where V
  e.The first derivative of the wave function must approach zero when approaching all regions of potential energy V > 0.

 

Question 2

Both the classical and quantum mechanical probability densities predict for a simple harmonic oscillator that
 

a. the probability of the particle being at that location will be greatest at regions of greatest potential energy.
  b. the particle has a finite probability of being in a region with V > E, where E is the total energy of the system.
  c. at very large values of n (the number of energy state), the particle will most likely be detected furthest from the equilibrium position within its classically defined range of motion
  d. the minimum energy of the oscillating particle is zero

[guyanai]

Answer to Question 1

e.
This statement is not true. It is not necessary for the first derivative to approach zero as the particle encounters a finite potential. In fact, there is a small probability that the particle will exist beyond the barrier, in the classically forbidden region. In that case, the first derivate would approach the value of the first derivative of the wave function inside the region of the potential.

Answer to Question 2

c.
At energies near the classical realm, both models predict the particle oscillating to be detected most oftenthat is, the highest probability of being at that pointfurthest away from the equilibrium point. The two must match up because of Bohr's correspondence principle.

[meagbuch]

Thank you!

[guyanai]

Always glad to help...