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location Valdosta, ga
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seen Sep 20 at 17:41

I am just a man who has an insatiable desire for knowledge.

"For the rest, brethren, whatever is true, whatever is worthy of reverence and is honorable and seemly, whatever is just, whatever is pure, whatever is lovely and lovable, whatever is kind and winsome and gracious, if there is any virtue and excellence, if there is anything worthy of praise, think on and weigh and take account of these things [fix your minds on them]."~ Philippians 4:8


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awarded  Autobiographer
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comment Determining the Wave Function From Initial Conditions
Oh, I see. You are using terminology that I am unfamiliar with. I still do not see how this relates to the wave function being only a mixture of the first two stationary states.
Aug
15
comment Determining the Wave Function From Initial Conditions
Well, I did not define them, but the textbook I am using does, which is Griffith's Introduction To Quantum Mechanics. Here is what he says regarding stationary states: "Although the wave function itself does (obviously) depend on $t$, the probability density, $|\Psi(x,t)|^2 = \Psi^* \Psi = \psi e^{i Et/\hbar} \psi e^{-i Et/\hbar} = |\psi(x)|^2$ does not.
Aug
15
comment Determining the Wave Function From Initial Conditions
So, what other justification could be used? The answer key does not use this operator, nor is it spoken of in the chapter from which this problem comes from.
Aug
15
comment Determining the Wave Function From Initial Conditions
@ACuriousMind I do not know of this time evolution operator of which you speak.
Aug
15
comment Determining the Wave Function From Initial Conditions
Yes, exactly. As far as I understand, the most general solution of the infinite well is $\Psi (x,t) = \sum_{n=1}^{\infty} c_n \psi_n(x) \phi_n(t)$, where the coefficients are $c_n = \sqrt{\frac{2}{a}} \int_{0}^{a} \sin(\frac{n \pi}{a} x) \Psi(x,t)$. Why wouldn't I use these two equations to calculate the wavefunction for all future times?
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asked Determining the Wave Function From Initial Conditions
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accepted Finding Interatomic Spacing
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asked Finding Interatomic Spacing
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comment How should a theoretical physicist study maths?
A very interesting response to the query.
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awarded  Notable Question
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awarded  Notable Question
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comment Collision Between Two Particles: Writing the Mass As A Function of The Angle
I don't believe this is a duplicate: I am asking for advice as to how I might write $\displaystyle \frac{m_1}{m_2}$ as a function of the angle (some angle); but the other question asks to verify unrelated equations.
Jan
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comment Collision Between Two Particles: Writing the Mass As A Function of The Angle
Well, I was defining $\theta$ as the angle between the final velocity vectors. Would this not be helpful?
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asked Collision Between Two Particles: Writing the Mass As A Function of The Angle