Recent content by cleggy

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    Ehrenfest theorem and Hamiltonian operator

    This makes no sense to me. I think I'm going to call it a day. Thanks for all your help Cyosis
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    Minimum and maximum uncertainty values in quantum harmonic oscillator

    I don't know how to find the time dependent expression for <x^2>
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    Ehrenfest theorem and Hamiltonian operator

    I'm still not following I'm given the commutation relations in my text as [x^2,p^2] = xxpp - ppxx = 2ih(bar)(xp + px) [xp,p^2] = xxpp - ppxx = 2ih(bar)(p^2) [px,p^2] = xxpp - ppxx = 2ih(bar)(p^2)
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    Minimum and maximum uncertainty values in quantum harmonic oscillator

    so i have to do a first derivative test
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    Minimum and maximum uncertainty values in quantum harmonic oscillator

    I've been going at this for so long now my mind is turning mushy
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    Minimum and maximum uncertainty values in quantum harmonic oscillator

    I don't know where the time dependence has gone I'm not sure how to calculate the minimum and maximum values of a function?
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    Minimum and maximum uncertainty values in quantum harmonic oscillator

    Homework Statement I have to find the minimum and maximum values of the uncertainty of \Deltax and specify the times after t=0 when these uncertainties apply. Homework Equations The wave function is Ψ(x, 0) = (1/√2) (ψ1(x)+ iψ3(x)) and for all t is Ψ(x, t) = (1/√2)...
    • cleggy
    • Thread
    • Harmonic Harmonic oscillator Maximum Minimum Oscillator Quantum Quantum harmonic oscillator Uncertainty
    • Replies: 8
    • Forum: Advanced Physics Homework Help
  8. C

    Quantum Scattering: Finding E0 & Estimating Fraction of Particles Transmitted

    Homework Statement A beam of particles, each of mass m and energy E0,is incident on a square potential energy well of width L and depth V0,where 0 <V0 < h(bar)^2\pi^2/2mL^2 . Outside the region of the well, the potential energy is equal to zero. Suppose that E0 is the lowest energy at which...
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    Ehrenfest theorem and Hamiltonian operator

    If [x^2,p^2] = xxpp - ppxx = 2ih(bar)(xp + px) Then how do I find the term (xp + px) ?
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    Ehrenfest theorem and Hamiltonian operator

    Which x and p ? the term (xp + px) ? I really thought i was on the right track. I'm not sure where to go now. Pointers?
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    What is the Time Evolution of a Particle in a Harmonic Potential Energy Well?

    that should have been |\Psi|^2 = [1/2][|\psi1|^2 + |\psi3|^2 + 2\psi1\psi3sin(2wot)]
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    Ehrenfest theorem and Hamiltonian operator

    According to my textbook the generalized Ehrenfest theorem is what you have put but without the derivative term of A at the end
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    What is the Time Evolution of a Particle in a Harmonic Potential Energy Well?

    Right so I should have |\Psi|^2 = 1/2 |\psi1|^2 + |\psi3|^2 + 2\psi1\psi3sin(2wot)
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    Ladder operators and harmonic oscillator

    with AA†A†A† I get \psi_{}n+2. The first to terms convert \psi_{}n into different eigenfunctions. Because \psi_{}n is orthonormal to these eigenfunctions, these terms can be dropped from the integral. Correct? Also since the lowering operator is first to act on the ground-state harmonic...
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    Ehrenfest theorem and Hamiltonian operator

    Homework Statement Use the generalized Ehrenfest theorem to show that any free particle with the one-dimensional Hamiltonian operator H= p^2/2m obeys d^2<x^2> / dt^2 = (2/m)<p^2>, Homework Equations The commutation relation xp - px = ih(bar) The Attempt at a Solution...