Where can I find information on solving for new energies using Dirac notation?

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Discussion Overview

The discussion revolves around solving for new energies in a quantum system using Dirac notation, particularly after the introduction of a new potential. Participants explore methods and concepts related to the Hamiltonian and potential energy terms.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Homework-related

Main Points Raised

  • One participant describes their problem set, indicating they have the initial energies and matrix elements but are unsure how to proceed to find the new energies after adding a new potential.
  • Another participant suggests solving the equation H|psi> = E |psi> for the new Hamiltonian, which includes both the old and new potentials.
  • A different participant expresses curiosity about potential tricks related to Dirac notation that might aid in the solution.
  • One participant proposes that perturbation theory might be relevant if the new potential is small compared to the old potential.
  • Another participant agrees with the suggestion of using perturbation theory and recommends checking Wikipedia for more information on Dirac notation.

Areas of Agreement / Disagreement

Participants express varying degrees of uncertainty about the best approach to take, with some suggesting perturbation theory while others are exploring different methods. No consensus is reached on a single method or solution.

Contextual Notes

There is an assumption regarding the size of the new potential in relation to the old potential, which may affect the applicability of perturbation theory. The discussion does not resolve whether perturbation theory is the best approach or if other methods might be more suitable.

theFuture
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So in my problem set I'm asked to solve for the "new energies of the system" I'm given the initial energies of this system and told a new potential is added. I know all the matrix elements. I solved for H|psi> so where do I go from here for the energies?
 
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I'm not sure, but can't you just solve H|psi> = E |psi> for the new Hamiltonian which is defined by

H=-hbar^2/2m Laplacian +Vold+Vnew
 
That's what I was thinking but I was curious if there was some other trick buried in the Dirac stuff. Thanks.
 
The lecturer might be asking you to use pertubation theory - is the new potential small compared to the old?


Kane
 
I think Kane is right.

You can check wikipedia about the Dirac notation.
 

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