SECTION B
13 Let us consider a particle of mass m in a one-dimensional potential given by (with a>0 ):
(a) Draw a sketch of the potential profile.
(b) Write the general wave-function of the particle for each region of the potential profile.
(c) What are the boundary conditions to be imposed at the interfaces between Region I and II
and Region I and III?
(d) Apart from a normalisation constant, what is the general wave-function of the whole
system?
(e) What are the energy levels of the system?
(f) How would these energy levels change if the potential barriers in Regions I and III were
suddenly removed?
SECTION B
13
Let us consider a particle of mass m in a one-dimensional potential given by (with a>0):
V(z)=0 0<x<a Region I V()=x<0 Region II V()=o xa Region III
(a) Draw a sketch of the potential profile.
[2]
(b) Write the general wave-function of the particle for each region of the potential profile. [4]
(c) What are the boundary conditions to be imposed at the interfaces between Region I and I and Region I and III? [2]
(d) Apart from a normalisation constant, what is the general wave-function of the whole system?
[5]
(e) What are the energy levels of the system?
[c]
(f) How would these energy levels change if the potential barriers in Regions I and Ill were suddenly removed? [4]