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Sup /sci /
On one of my problem sets for quantum mechanics there is a case where a particle in a potential well (V= infinity for |x|>=x0) at t=0 is described by the wave function ψ (0,x)=N(x-x0)(x+x0)
Does that even make sense physically? I mean it's not even an eigenfunction of the Hamilton operator
>inb4 no homework threads: the only thing I had to do was normalize ψ which I already did
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>>8964826
Yeah, it makes sense. You're right that it's not an eigenfunction but it doesn't need to be if you're just considering a wavefunction frozen in time.
That function is a superposition of the eigenstates of the potential well, if you take the inner product of that function with an eigenstate then you get the amplitude of that eigenstate in the superposition.
So if [math]|\alpha\rangle[/math] index the eigenstates of the well then any wavefunction in that environment can be written as:
[eqn]|\psi\rangle=\sum_\alpha\langle\alpha|\psi\rangle|\alpha\rangle
[/eqn]where, in the case of spatial wavefunctions:
[eqn]\langle\alpha|\psi\rangle=\int^\infty_{-\infty}\alpha^*(x)\psi^*(x)\text{d}x
[/eqn]
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>>8966329
oops, the psi shouldn't be starred in that integral
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>>8964826
Here is something I don't understand.
Schrodinger's Cat is not a paradox. The particle will be in a super position until it interacts with the poison-dispensing detector. Once it is detected, the wave function collapses. And then the cat is either alive or dead, only one or the other before you even open the box.
Why did Schrodinger not realize this immediately?
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>>8966388
lazy troll is lazy
kys
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>>8966428
I want answers, not memes.
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