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Operators implementation with operators

  1. Oct 9, 2015 #1
    Hello I may make some mistakes because I am not professional at physics:smile:.So I want to know how to
    implementate wave function with operators example:p(hat) impletated with ψ so: p(hat)ψ=pψ so as you saw it was momentum operator and momentum operator is:-iħ∂/∂x as you saw it is one diemensional momentum operator.So we have ψ one dimensional so we have ψ(x) and ψ(x)=A sin(kx)+B cos(kx) and we have -iħ∂/∂x A sin(kx)+B cos(kx) is it right and does implement wave function with operator have numeral solution?
     
  2. jcsd
  3. Oct 9, 2015 #2

    blue_leaf77

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    That's only true if ##\psi## is an eigenfunction of the momentum operator, but since in your problem you seem to have assumed that ##\psi(x) = A\sin kx + B\cos kx## which is a superposition of different momentum operator eigenfunctions, your relation "p(hat)ψ=pψ" cannot hold anymore. If what you want is just to operate ##i\hbar \partial/\partial x## on to ##\psi(x)## then just do as the operator told you, that is , partial differentiation.
    I'm not sure what you meant by "numerical solution". Since it is a function (in position space), you can always calculate its value at any given point ##x##.
     
  4. Oct 9, 2015 #3
    Thank you that information helped me a lot.On numerical solution I thoughte like that ψ=3.62 or some other imaginary- and negative- number
     
  5. Oct 9, 2015 #4

    blue_leaf77

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    Your wavefunction is a function of x, to say that ##\psi## has certain value you need to know x (and the other constants). Moreover for real ##\psi## at some point ##x##, its value cannot be bigger than one as the wavefunction must be normalized.
     
  6. Oct 9, 2015 #5
    Your information helped me a lot thank you very much(;
     
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