- #1
lazyluke
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Homework Statement
Hi, The problems asks to calculate multiple things for a Gaussian wave packet. Steady state function: psi(x,0)=A*exp(-ax^2).My problem is that I'm stuck at calculating <p^2>.
Homework Equations
<p^2>=Int(|psi|^2*(-1*h^2*d^2/dx^2))dx or
<p^2>=Int(psi*(-1*h^2*d^2/dx^2(psi-conjugate)))dx ?
I am not sure if I can use the expression for |psi|^2- which is already defined and I think calculating the second expression will be wrong since it will give us an answer with i and t sine the exponent from complex conjugate of psi will come down or am i wrong?
The Attempt at a Solution
I know I'm doing something wrong since after i evaluate integrals I get:
<p^2>=4*(2/m)^(1/2)*w^6h^2*(4w^2*(pi/w^6)^(1/2)-2(1/2(pi/w^2)^(1/2)) where w=(a/(1+(2ihat/m)^2)^1/2 which cancels out to 0, somehow I should get ah^2. Now I'm not sure is I should use <p^2>=Int(|psi|^2*(-1*h^2*d^2/dx^2))dx where its a second derivative of |psi|^2 or <p^2>=Int(psi*(-1*h^2*d^2/dx^2(psi-conjugate)))dx where the second derivative is only of the complex conjugate and not the |psi|^2. Or I should not use the w just use the expression defined above? (I thought since w is independent of x it would not matter). Any help will do, just before Sunday evening as its due on Monday morning.
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