SME
Physical Chemistry II: Quantum & Spectroscopy · Problem type
Eigenfunction of which operator?
Use this for “Is cos 5x an eigenfunction of d/dx? Of d²/dx²? If so, what is the eigenvalue?”
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Which operators give back this function times a number?
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Take the derivative once and see whether f comes back times a number; if not, take it again.
Assumptions
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f is an eigenfunction when the operator gives back f times a number, the eigenvalue.
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An eigenfunction of d/dx is also one of d²/dx², since taking the derivative twice multiplies by the number twice.
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The momentum operator is −iħ d/dx and the kinetic energy operator is −(ħ² ÷ 2m) d²/dx².
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