All Questions
Tagged with wavefunction operators
292
questions
0
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85
views
How do operators on kets and wavefunctions correspond?
Let $\hat{A}$ be an operator on Hilbert space vectors. How does one show that there always exists a corresponding operator $\hat{a}$ on wave functions? i.e. $\exists \hat{a}:L^2\rightarrow L^2$ s.t. $$...
- 65
0
votes
2
answers
88
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The eigenvectors associated to the continuous spectrum in Dirac formalism
I am comfused about the definition of an observable, eigenvectors and the spectrum in the physics litterature. All what I did understand from Dirac's monograph is that the state space is a complex ...
- 173
7
votes
3
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397
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Negative kinetic energy on a step potential
I'm doing an introductory course on quantum mechanics. I'm having trouble with the explanation of the kinetic energy on the classically forbbiden region on a step potential ($V=0$ for $x<0$, $V=V_0$...
- 73
1
vote
1
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108
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Can the Parity Operator in polar coordinates be defined as $\hat\Pi\psi(r,\theta,\phi) = \psi(r,\theta+\pi,\phi).$?
I was reading about Symmetries & Conservation Laws from Introduction to Quantum Mechanics, David J. Griffiths when I came across this question about the parity operator in three dimensions:
...
- 13
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26
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Classical Hamilton’s equations in quantum mechanics [duplicate]
How can one derive what the position operator is in momentum space for a quantum wave function from the classical Hamilton’s equations?
Similarly, is a concept of an “angular momentum space�� ...
- 1
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40
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If an electron is inside an atom, does the expected value of spin measurements also depend on the orbital wavefunction?
The total quantum state of an electron in an atom can be written as the product of the orbital wavefunction and a spinor representing its spin state, $\Psi = \psi(r,\theta,\phi) \otimes \chi$. Say you ...
- 1,775
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2
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79
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Definition of expectation value for momentum [duplicate]
I think this is probably a stupid question but I'm confused over how the expectation value for momentum is calculated. It is always given as $$⟨𝑝⟩ = ⟨𝜓|\hat{p}𝜓⟩ = −𝑖\hbar∫𝜓^*(𝑥)\frac{d𝜓(𝑥)}{...
-1
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1
answer
89
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How to calculate the inner product $ \langle T|x \rangle = \langle\frac{p^2}{2\mu} |x\rangle$? [closed]
If I have a wave function $ \psi (x) = \langle x|\psi \rangle$, now I want to use kinetic energy representation $$ T = \frac{p^2}{2\mu} ,$$ where $ \mu $ is the mass of particle. I try to
\begin{align*...
- 37
-2
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1
answer
55
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Uncertainity in position in 1D potential box
In a question of a usual 1D box for a particle between $-L/2$ to $L/2$ i had to compute $\Delta x$ and $\Delta p$ for the particle. The solution used the formulas-
$$\Delta x = \sqrt{\langle x^2 \...
- 367
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1
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83
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Operators algebra for quantum mechanics [closed]
I am taking my first quantum mechanics course and I am a bit lost in operators algebra. These are the main questions I have:
Why can we write this kind of equations? $$ Ô \psi = o\psi $$
What I mean ...
0
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5
answers
183
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Difference between the expectation value of an operator and operator applied to wave function?
Expectation value of any operator $\hat{Q}$ is defined as,
$$
\left\langle\psi_n\mid\hat{Q}\mid \psi_n\right\rangle
$$
and action of the operator $\hat{Q}$ on wavefunction is defined as
$$
\hat{Q} \...
- 390
0
votes
0
answers
109
views
Functional analysis question about operator on quantum wave functions
If I have two time-independent wave functions $\psi_{t_{1}}$ and $\psi_{t_{2}}$ and define an operator $\hat{U}$ such that $$\psi_{t_{2}} = \hat{U}_{t_{1},t_{2}}(\psi_{t_{1}})$$ and $$\psi_{t_{2}}(x) =...
- 111
0
votes
1
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80
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Momentum probability density and its normalization
Let the (normalized) wave function $\Psi(x,y)$ represent a free particle in the XY plane. I know $|\Psi|^2$ gives me the probability density function of the particle's position, which I can then ...
- 1,616
1
vote
1
answer
40
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What will be wave function after application of operator?
In the mathematical treatment of quantum mechanics, we have a wave function ($ψ$) that helps us to know the different information (like position, velocity, energy, etc.). To measure such a quantity we ...
-3
votes
2
answers
159
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Position operator action on a wavefunction [closed]
In a 1 dimensional infinite potential well with width $a$, the ground state wave-function is given by
$$\psi(x) = \sqrt{\frac{2}{a}}\sin(\frac{\pi}{a}x)$$
The action of the position operator in the ...
- 113