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Consider the energy eigenstates of a particle in a quantum harmonic oscillator with frequency ω.

a) Write down expressions for the energies of the three lowest states.
b) Sketch the potential for this system, along with the position of the three lowest energy levels.
c) Add to your sketch the form of the wavefunction and the probability density in the three lowest energy states.

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Question A3 Consider the energy eigenstates of a particle in a quantum harmonic oscillator with frequency w. a) Write down expressions for the energies of the three lowest states. b) c) Sketch the potential for this system, along with the position of the three lowest energy levels. Add to your sketch the form of the wavefunction and the probability density in the three lowest energy states. [10 marks]
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