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Linear combination of phi(n)

  1. Feb 9, 2004 #1


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    please refer to the attachment

    in the last part, it states that...

    If solutions phi.n.(r) can be found, for different values of En, then the linear combination is also a solution of the Schroedinger equation, because the Schroedinger equation is a linear equation. However, such a linear combination does not represent a particle with a well defined energy.

    if it is not represent a particle with a well defined energy, then what is it represent?

    does it represent all the energy states from ground state to En?

    thx for answering

    Attached Files:

  2. jcsd
  3. Feb 9, 2004 #2
    Let i be the energy representation
    Transforming to the position representation j

    So a superposition of the states of definite energy represents a state with the probability <i|psi> of having energy E_i.

    So the Schrodinger equation (the equation which governs the dynamics of the wave equation in the language of position space) must be linear for it to give a correct representation of the quantum system.
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