Answer to Question #94382 in Quantum Mechanics for prashanth

Question

A particle of mass m and energy E is moving in the potential

V(x,y,z)=0, z<0
V(x,y,z)=Vo, z0.

Assume E>Vo>0.
(a) It the particle is incident from z<0
perpendicular to the z-axis, what is the
probability that it will penetrate to z>0?

Assume E<Vo>0
(b)Measure tunneling probability in the above case?

Answer 1

 

(a)   the probability is equal to zero because the energy of particle l E less then Vo (E<Vo)

(b) the tunneling probability is given by formula

$ψ(x) =Ce^{ βx}$

where

$β^2=2m^2(V_0−E)$