[MOB/QM-080001]

A particle of mass \(m\) moves in a two dimensional potential\(V(x,y)=\frac{1}{2}\big(4x^2+ y^2\big)\) and is in an energy eigen state of energy \(E=\frac{5}{2}\hbar\omega.\) The corresponding un-normalized eigen function is

1. \(\psi_1(x) = y \exp\big(-\frac{m\omega}{\hbar}(2x^2 + y^2) \big)\) \Label{ANS}
2. \(\psi_1(x) = xy \exp\big(-\frac{m\omega}{\hbar}(2x^2 + y^ 2) \big)\)
3. \(\psi_1(x) = x \exp\big(-\frac{m\omega}{\hbar}(2x^2 + y^ 2) \big)\)
4. \(\psi_1(x) = y \exp\big(-\frac{m\omega}{\hbar}(x^2 + y^2) \big)\)

Answer (a)

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