Undergrad Find the energy from the graph of the wave function

[HastiM]

Hello,

I am wondering if it is possible to determine the kinetic energy and potential energy of a quantum system just by investigating the graph of its wave function. Suppose we are given the graph of some wave function Ψ(x), i.e. a function which is an eigenfunction of the hamiltonian. I think its second derivative Ψ''(x) should somehow correspond to the kinetic energy of the particle. Is that right? What about the potential energy?

Best regards

 

[BvU]

Yes, $\displaystyle {-{\hbar^2\over 2m}\nabla^2}$ is the kinetic energy operator.

Eigenfunctions of the Hamiltonian have eigenvalues corresponding to the total energy $T+V$ .

So, only if you have the second spatial derivative and the time derivative can you deduct $V$