Recent content by Cracker Jack

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    Adiabatic expansion of infinite square well

    Homework Statement Suppose that an infinite square well has width L , 0<x<L. Nowthe right wall expands slowly to 2L. Calculate the geometric phase and the dynamic phase for the wave function at the end of this adiabatic expansion of the well. Note: the expansion of the well does not occur at...
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    Prove Quantum Spin Problem: θ, Su11, Su22, Sz1, Sz2, Sx2

    I get zero for both terms, with σz=[(1,0),(0,-1)] (the 2x2 form) (0,1)*[(1,0),(0,-1)] =(0,-1) then (0,-1)*(1,0)=0
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    Prove Quantum Spin Problem: θ, Su11, Su22, Sz1, Sz2, Sx2

    Homework Statement It was noted that <00|Su11Su22|00> = -ħ2/4 * u1⋅u2. where u1 and us are unit vectors along which the two spin operators are measured and θ is the angle between. |00> is the singlet state that the two electrons are entangled in (corresponding to total spin values ). Prove...
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    How do I evaluate <x> with the k-space representation?

    Thank you this helped a lot, and now I think I've gotten the right answer.
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    How do I evaluate <x> with the k-space representation?

    Thank you, I think this helps. I was thinking x could only act on Ψ if it was Ψ(x,t). Looking through lecture notes, I think that x operates in k space as i∂/∂k. Is that correct?
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    How do I evaluate <x> with the k-space representation?

    Homework Statement Given the following k-space representation of the wave function: Ψ(k,t) = Ψ(k)e-iħk2t/2m use the wave number representation to show the following: <x>t=<x>0 + <p>0t/m <p>t=<p>0 Homework Equations <x>=∫Ψ*(x,t)xΨ(x,t)dx <p>=∫Ψ*(x,t)(-iħ ∂/∂x)Ψ(x,t)dx The Attempt at a...