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Conservation of energy

  1. Oct 8, 2015 #1
    Hi guys! one quick question, if in a quantum system the hamiltonian of a particle evolves with time (let's say, the potential is a function of t), the energy is not conserved right? I just want to be sure about this, thanks!
  2. jcsd
  3. Oct 8, 2015 #2
    Then, where the energies gone? Whether the Hamiltonian is time-dependent, Schrodinger equation gives constant energy.
  4. Oct 8, 2015 #3
    But if you think of the hamiltonian as a matrix, that means that the matrix has different matrix elements for every different time, therefore its eigenvalues are not the same as time evolves.
  5. Oct 8, 2015 #4
    Then, the wave function have to vary depending on time to keep the energy as constant.
  6. Oct 8, 2015 #5
    Ok, but think about a non translationally invariant system. Momentum is not conserved in such a system because translation invariance is broken. If you break rotation invariance, angular momentum is not conserved in such a system, and if you break time invariance, then energy shouldnt be conserved.
  7. Oct 8, 2015 #6
    If it breaks the time translational invariance, then yes. It may come from
    [tex] \dfrac{\partial}{\partial t} \int dV \psi^*(x,t) \hat{H}(x,t) \psi(x,t) ,[/tex]
    and it is not vanishing in general. Then, the energy can't conserved.

    I confused with the stationary solution in quantum mechanics textbook. Sorry for that.
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