The wavefunction for a particle in a infinite, one dimensionalpotential well of

Question

The wavefunction for a particle in a infinite, one dimensionalpotential well of width L is: (x) = 1/6 [2/L]^1/2 (sin x/L + 2sin 2x/L + 3 sin 3x/L) What is the eigenvalue of the Hamiltonian operator for eacheigenstate. I have an exam and this is a practice exam. Please helpin solving this. Thanks alot. The wavefunction for a particle in a infinite, one dimensionalpotential well of width L is: (x) = 1/6 [2/L]^1/2 (sin x/L + 2sin 2x/L + 3 sin 3x/L) What is the eigenvalue of the Hamiltonian operator for eacheigenstate. I have an exam and this is a practice exam. Please helpin solving this. Thanks alot.

Explanation / Answer

is amixture of two energy eigenstates, with energies E 1 =p 2 1 2mand E 1 =p 2 1 2m. Anenergy eigenstate with eigenvalue E i willhave a time dependence e iE i t/¯ h Therefore, the u 1 partof has anenergy dependence e iE 1 t/¯ h andthe u 2 part ofhas an energy dependence e iE 2 t/¯ h (x,t) = 1 2 u 1 (x)e iE 1 t/¯ h +u 2 (x)e iE 2 t/¯ h

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