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The Hamiltonian for the linear harmonic oscillator can be written ... , in units with ... . The eigenstates are given by ... , ... , ... , where ... is a Hermite polynomial. An alternative reformulation of the problem can be based on the representation ... in terms of ladder operators ... and ... . The step-down or annihilation operator ... acts on the eigenfunctions according to ... , with ... . The step-up or creation operator ... satisfies ... In this Demonstration, the eigenfunction ... is plotted in black. Also shown is either ... in red or ... in blue.

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      EUN,LOM,LRE4,work-cmr-id:397249,http://demonstrations.wolfram.com:http://demonstrations.wolfram.com/LadderOperatorsForTheHarmonicOscillator/,ilox,learning resource exchange,LRE metadata application profile,LRE

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