Question

Let a particle of mass m be found in a potential well, widths a in the state ψ (x) =1/√5φ1 (x) +i/√5φ2 (x) + √3/√5φ3 (x), where  φ(x) are Hamiltonian's own states. If we measure energy, what values ​​do we obtain and with what probability?

Answer 1

The given wavefunction is a superposition of eigen states of hamiltonian and is normalized. If we measure energy of system it collapses to  any of the eigen states and we get the energy corresponding to that eigen state. Given that

 ψ (x) =1/√5 φ1(x) +i/√5 φ2(x) + √3/√5 φ3(x) corresponding energy eigen value is given by 

implies that the prpbability of getting energy eigen value E1 is 1/5, where

Probability of getting E2 is also 1/5 where

and P(E3) = 3/5 where