Quantum Harmonic Oscillator — CSIR Net PYQ (Question 10)

Question

Let a=\frac{1}{\sqrt{2}}(x+ip) and {a}^{\dagger }=\frac{1}{\sqrt{2}}(x- ip) be the lowering and raising operators of a simple harmonic oscillator in units where the mass, angular frequency and \hbar have been set to unity. If |0\rangle is the ground state of the oscillator and \lambda is a complex constant, the expectation value of \langle \psi |x|\psi \rangle in the state |\psi \rangle =exp\left( \lambda {a}^{\dagger }- {\lambda }^{∗}a \right)|0\rangle, is

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Option 4

Quantum Harmonic Oscillator — CSIR Net PYQ (Question 10)

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