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Energy definition

  1. Jan 25, 2007 #1
    How is energy defined in quantum mechanics?is it defined by the De-Broglie relations or from the eigenvalue equation of H operator?Are the two somehow equivalent?
  2. jcsd
  3. Jan 25, 2007 #2


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    Interesting question. Actually we have the energy observable (that is what is measured) and the Hamilton operator. If we measure the energy of a quantum system we should get a value from the operator's spectrum.

    The measurement problem is really tricky and under debate, but energy is always associted to the hamiltonian.
  4. Jan 25, 2007 #3
    What is the status of the De-Broglie relations then?Is it a derived result or an axiom?does it always hold?
  5. Jan 25, 2007 #4
    It is derived. It doesn't always hold, because it really only applies to particles in free space. If there is a non-constant potential present, then you cannot necessarily even assign a single "wavelength" to the eigenstates (only a spectrum of them). For example, the Hydrogen atom's ground state is exponentially decaying with radius.
  6. Jan 25, 2007 #5
    so the de-broglie relation holds only for constant potential,is that what you are saying?what is the definiton of energy then?
  7. Jan 25, 2007 #6
    Let me turn this around a bit -- what do you think the definition of energy in classical mechanics is?
  8. Jan 25, 2007 #7
    ummm...a quantity that remains conserved because the lagrangian is time-independent?
    can anyone please give me a sort of outline how i can derive the De-broglie relation for energy ?
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