How Can Quantum Mechanics Constants Be Deduced from Average Energy?

[greisen]

Hey,

I have a normalized wave function

PSI = c_1 psi_1(x) + c_2 psi_1(x)

where c_1 and c_2 are constants with the eigenfunctions equal to ground and first excited state. The average energy of the system is pi^2hbar^2/(ma^2) - what can one deduce about the constant and how?

Thanks in advance

 

[OlderDan]

Hey,

I have a normalized wave function

PSI = c_1 psi_1(x) + c_2 psi_1(x)

where c_1 and c_2 are constants with the eigenfunctions equal to ground and first excited state. The average energy of the system is pi^2hbar^2/(ma^2) - what can one deduce about the constant and how?

Thanks in advance

I'm thinking energy expectation value, similar to your problem on creation/anihiliation. What are the eigenenergies of the two states?

 

[greisen]

The particle is in a one dimensional well with V(x) = 0 for o <= x <= a and otherwise it is infinity. Is it a linear combination between the two states ?

Again thanks very much

 

[OlderDan]

The particle is in a one dimensional well with V(x) = 0 for o <= x <= a and otherwise it is infinity. Is it a linear combination between the two states ?

Again thanks very much

Yes it is a linear combination of states. With orthonormal basis functions and normalized PSI the sum of the squares of the coefficients has to be 1. The products of coefficients times eigenenergies has to be the total energy