Consider a two-dimensional harmonic oscillator with potential energy V(x, y) = 1/2kx x² + 1/2ky y² If ψnx(x)… · ABC26PH0147

Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Harmonic Oscillator · Exam: CSIR NET 2013 · Marks: 2 · Difficulty: Medium

Consider a two-dimensional harmonic oscillator with potential energy
$V(x, y) = \frac{1}{2}k_x x^2 + \frac{1}{2}k_y y^2$
If $\psi_{nx}(x)$ and $\psi_{ny}(y)$ are the eigensolutions and $E_{nx}$ and $E_{ny}$ are the eigenvalues of harmonic oscillator problem in x and y direction with potential $\frac{1}{2}k_x x^2$ and $\frac{1}{2}k_y y^2$ respectively, the wave function and eigenvalues of the above two-dimensional harmonic oscillator problem are
(a)$\psi_{n_x,n_y} = \psi_{n_x}(x) + \psi_{n_y}(y)$, $E_{n_x,n_y} = E_{n_x} + E_{n_y}$
(b)$\psi_{n_x,n_y} = \psi_{n_x}(x) \cdot \psi_{n_y}(y)$, $E_{n_x,n_y} = E_{n_x} \cdot E_{n_y}$
(c)$\psi_{n_x,n_y} = \psi_{n_x}(x) \cdot \psi_{n_y}(y)$, $E_{n_x,n_y} = E_{n_x} + E_{n_y}$
(d)$\psi_{n_x,n_y} = \psi_{n_x}(x) + \psi_{n_y}(y)$, $E_{n_x,n_y} = E_{n_x} \cdot E_{n_y}$
Answer
Answer (as printed): C
Explanation
No explanation was printed for this question.

Study loop for Quantum Chemistry

1. Practise the PYQsPrevious-year questions, with answers

· Browse this chapter in the app