IN QUATUM MECHANICAL SIMPLE HARMONIC OSILLATOR a How does th

IN QUATUM MECHANICAL SIMPLE HARMONIC OSILLATOR

a) How does the number of nodes in the probably density function change as the quantum number increases? b) How does the lateral extent of the probability density function change as the quantum number increases? c) How does the probability of finding the mass in a classically forbidden region change as the quantum number increases?

Solution

a) The number of nodes is equal to the quantum number, for ground state n=0 no node exist.

b) As the quantum number increases, the lateral extent increases as it will have more nodes.

c) As the quantum number increases the agreement btween the clasical and quantum probabilities imrpoves, they are more closure. The probability of finding the particle in classically forbidden region decreases, this is in accordance to the correspondence principle.