Question

For the particle in a ring, how many nodes are there in the imaginary part of the wave function over the range 0 to 2π when ml=0? What about ml=3? (A) 0 and 3, respectively (B) 1 and 3, respectively (C) 0 and 2, respectively (D) 1 and 4, respectively (E) 0 and 6, respectively.

Answer 1

A) 0 and 3 respectively.

For a particle on a ring the wavefunction is given by $\psi=N*e^{i*m_l*\phi}*(-1)^{2m_l}$

Now when $m_l=0$

Nodes are when the wavefunction is at zero on the x axis.

So $\psi=N*e^{i*0*\phi}*(-1)^{2*0}=N*1*1 \neq 0$

Hence there are no nodes for $m_l=0$

Now for

m- 3

N(cos(3 *

Now the nodes of the imaginary part from 0 to $2\pi$ is 3 (since when we draw a sine function from zero to $2\pi$ we have 3 nodes