Formalism of Quantum Mechanics and One Dimensional Problems

Abstract

Let Â=Â^† be an observable operator with a complete set of eigenstates |ϕ _n 〉 with eigenvalues α _n (n=0, 1, 2,...). A generic state is given by

$$\left. {|\psi } \right\rangle = \left. {N(3|{\psi _1}} \right\rangle \left. { - 4i|{\psi _2}} \right\rangle )$$

where |ψ₁〉,|ψ₂〉 are orthonormal. Find N and the probability P ₄ that a measurement of  yields α₄. What does it happen in case of degeneracy? Specialize these calculations to the case |ϕ _n 〉=|ψ _n 〉.