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- Express the operators $a$ and $a^\dagger$ defined by $$ a = {( p -i m\omega x) \over \sqrt{2m\omega \hbar}}, \qquad a^\dagger = {( p +i m\omega x) \over \sqrt{2m\omega \hbar}} $$ in the co-ordinate representation and solve the equation $$ a \psi(x) = 0 $$ to determine the ground state wave function.
- Applying $a^\dagger$ on the ground state wave function, find the first two excited state eigen functions for the harmonic oscillator.
- Normalize the ground state and the two excited state eigen functions found above.
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4727:Diamond Point
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