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Jun 1, 2020 at 19:20 comment added Alfred Centauri @ThePointer, I wrote an answer that you might find helpful with regards to the quesiton in your comment.
Jun 1, 2020 at 18:27 vote accept The Pointer
Jun 1, 2020 at 18:18 comment added user87745 @ThePointer E is the energy of an eigenstate of the Hamiltonian, in particular, the $\psi(r)$. You can describe a particle which can be in a superposition of multiple such eigenstates and thus doesn't have a specific energy. But yes, if you want to describe a particle that has a specific energy, the E would be the energy of that particle and the spatial part of the wavefunction would have to follow the eigenvalue equation of the Hamiltonian (the last equation in my answer) with the eigenvalue E.
Jun 1, 2020 at 17:57 comment added The Pointer Thanks for the answer. So $E$ is the energy of the system (such as the particle in question, if that's what we use the Shrödinger equation to model)?
Jun 1, 2020 at 17:34 comment added user87745 @A.Bordg Many thanks for the correction. :)
Jun 1, 2020 at 17:33 history edited user87745 CC BY-SA 4.0
deleted 153 characters in body
Jun 1, 2020 at 17:29 comment added A. Bordg As a result there is a problem with your second line.
Jun 1, 2020 at 17:25 comment added A. Bordg Using two lowercase psi's is confusing.
Jun 1, 2020 at 17:02 history answered user87745 CC BY-SA 4.0