A one-dimensional harmonic oscillator carrying a charge -q is placed in a uniform electric field $$\overrightarrow {\bf{E}} $$ along the positive X-axis. The corresponding Hamiltonian operator is

A) $$\frac{{{\hbar ^2}}}{{2m}}\frac{{{d^2}}}{{d{x^2}}} + \frac{1}{2}k{x^2} + qEx$$ B) $$\frac{{{\hbar ^2}}}{{2m}}\frac{{{d^2}}}{{d{x^2}}} + \frac{1}{2}k{x^2} - qEx$$ C) $$ - \frac{{{\hbar ^2}}}{{2m}}\frac{{{d^2}}}{{d{x^2}}} + \frac{1}{2}k{x^2} + qEx$$ D) $$ - \frac{{{\hbar ^2}}}{{2m}}\frac{{{d^2}}}{{d{x^2}}} + \frac{1}{2}k{x^2} - qEx$$

Answer & Solution

Correct Answer: Option D

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A one-dimensional harmonic oscillator carrying a charge -q is placed in...

A one-dimensional harmonic oscillator carrying a charge -q is placed in a uniform electric field $$\overrightarrow {\bf{E}} $$ along the positive X-axis. The corresponding Hamiltonian operator is

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