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If there is something fundamentally wrong in my understanding of quantum mechanics, pardon me for I have just started learning it.

We know that if we can come up with a solution for Schrodinger Equation of a Harmonic Oscillator, then we can generate further solutions by acting on it with the raising operator or lowering operator. These solutions turn out to be rungs of a ladder since we fix the “lowest rung” as the one which if acted on by the lowering operator should be equal to zero. This solution corresponds to an energy ℏω\2. But the ladder has only those rungs just because we have limited the lowest rung in such a way. Why not we have a state which when acted on by the lowering operator goes Negative i.e., some state with energy somewhere between zero and ℏω\2, why such a state is not allowed?

Regards,

Raja R K

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# Quantum Harmonic Oscillator - Why we limit the bottom end of the ladder

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