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Nov
24
comment Heuristics behind Dirac delta function in Master equation for probability?
Excellent! But for completing your answer, how would you derive the differential equation intuitively?
Nov
13
revised Heuristics behind Dirac delta function in Master equation for probability?
added 42 characters in body
Nov
6
asked Heuristics behind Dirac delta function in Master equation for probability?
Oct
21
accepted Prove that if $\hat H | a_n\rangle=a_n|a_n\rangle$, then $f(\hat H)| a_n\rangle=f(a_n)|a_n\rangle$
Sep
5
comment Can a baseball travel through the Sun?
@Alex It seems that you want the conditions under a ball could pass through the sun. I suggest to edit your question. Also, your question is quantifiable, you could make a short calculation to get the answer.
Sep
5
answered Twins Paradox - Does ageing depend on motion?
Sep
5
comment Continuum analogue of $ \langle \psi | \psi \rangle = \sum _i a_i^* a_i$
@qfzklm Of course not. $|i\rangle$ is just a discrete basis of the Hilbert space. This means (1)-(3).
Sep
4
comment Continuum analogue of $ \langle \psi | \psi \rangle = \sum _i a_i^* a_i$
@qfzklm "This is similar...": what do you mean by that? How do you define your $\psi(x)$ in terms of $|\psi\rangle$?
Sep
4
comment Wavefunctions in different Hilbert spaces
@Timaeus is right, there aren't lots of different Hilbert spaces, but there are lots of different basis, say $\{|x\rangle\}$ or $\{|p\rangle\}$. And BTW, $\psi(x,y):=\langle x, y |\psi \rangle$.
Sep
4
comment Wavefunctions in different Hilbert spaces
@march Actually, the correct expression would be writing $| \psi \rangle$ at the left hand side (without the $x$ in $\psi(x)$, because $| \psi \rangle$ does not depend on x, but when you project at the position space you have: $\psi(x):=\langle x| \psi \rangle$).
Sep
4
asked Prove that if $\hat H | a_n\rangle=a_n|a_n\rangle$, then $f(\hat H)| a_n\rangle=f(a_n)|a_n\rangle$
Sep
3
comment Continuum analogue of $ \langle \psi | \psi \rangle = \sum _i a_i^* a_i$
@user12262 I think I understood your comment. You're just saying that in your notation, the derivation of the result would be more clear, right? By the way, the derivative $d/dx$ of the definite integral $\int_a^b f(x)dx$ (with $a$ and $b$ constants) is zero because when you make the integral, you get just a constant. I think you referred to the fundamental calculus theorem by this: $(d/dx)\int_a^xf(x')dx'=f(x)$, which is not the same as the first derivative. Nevertheless I understood your point.
Sep
2
comment Continuum analogue of $ \langle \psi | \psi \rangle = \sum _i a_i^* a_i$
@ACuriousMind I'm not asking for you to check my work. I'm asking for experience in this problem, I have no clear idea of what it asks for. Therefore your comment is not constructive.
Sep
2
comment Continuum analogue of $ \langle \psi | \psi \rangle = \sum _i a_i^* a_i$
@qfzklm When I said "maps to" I meant from the discrete case to the continuum case (talking about spectrum of eigenstates). I don't understand the reason you say $a_i$ are constants, actually they are constants but I think that has noting to do with my question. And of course $| \psi \rangle$ maps to $\psi(x)$ when you take $\langle x| \psi \rangle$.
Sep
2
comment Continuum analogue of $ \langle \psi | \psi \rangle = \sum _i a_i^* a_i$
@user12262 Can you suggest me a book where I can find your replacement, please? I've never seen why is that possible or where it comes from. Thanks in advance!
Sep
2
asked Continuum analogue of $ \langle \psi | \psi \rangle = \sum _i a_i^* a_i$
Jun
18
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12
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