Derive an equation for the expectation value

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Reference no: EM133239017

Case: Consider a particle in a state given by the function Y(x) = y1(x) + y3(x), which is a linear combination of two eigenfunctions of the particle-in-a-box Schrödinger equation, y1(x) and y3(x).

a) Show that Y(x) is not an eigenfunction of the particle-in-a-box Hamiltonian

b) Derive an equation for the expectation value of the particle-in-a-box Hamiltonian, , for Y. You might find it useful to invoke the property of orthogonality for eigenfunctions of a Hermitian operator. Compose the result in terms of E1, the energy of the n = 1 state.

Reference no: EM133239017

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