Question

A particle of mass m is moving in the potential
\[ V(x) = \begin{cases} V_0 + \frac{1}{2} m \omega_{0P}^2 x^2 & \quad \text{if } x > 0 \\\infty & \quad \text{if } x \leq 0 \end{cases}\]
Figures P, Q, R, and S show different combinations of the values of \( \omega_0 \) and \( V_0 \).

Let \( E^{(P)}_j \), \( E^{(Q)}_j \), \( E^{(R)}_j \), and \( E^{(S)}_j \) with \( j = 0, 1, 2, \ldots \), be the eigen-energies of the j-th level for the potentials shown in Figures P, Q, R, and S, respectively. Which of the following statements is/are true?

• A. \( E^{(P)}_0 = E^{(Q)}_0 \)
• B. \( E^{(Q)}_0 = E^{(S)}_0 \)
• C. \( E^{(P)}_0 = E^{(R)}_0 \)
• D. \( E^{(R)}_0 \neq E^{(Q)}_0 \)

Answer 1

The Correct Option is B, C, D

The correct Answers are (B):\( E^{(Q)}_0 = E^{(S)}_0 \),(C):\( E^{(P)}_0 = E^{(R)}_0 \),(D):\( E^{(R)}_0 \neq E^{(Q)}_0 \)