ABC26PH0147 · Quantum Chemistry

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
\[ V(x,y)=\dfrac{1}{2}k_x x^{2}+\dfrac{1}{2}k_y y^{2} \]
If $\psi_{n_x}(x)$ and $\psi_{n_y}(y)$ are the eigensolutions and $E_{n_x}$ and $E_{n_y}$ are the eigenvalues of harmonic oscillator problem in $x$ and $y$ direction with potential $\dfrac{1}{2}k_x x^{2}$ and $\dfrac{1}{2}k_y y^{2}$ 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.

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