All Questions
Tagged with wavefunction complex-numbers
129
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2
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Time derivative of complex conjugate wave function [duplicate]
We have
$$\frac{\partial \Psi}{\partial t} = \frac{i\hbar}{2m} \frac{\partial^2 \Psi}{\partial x^2} - \frac{i}{\hbar}V\Psi$$$$\frac{\partial \Psi^*}{\partial t} = -\frac{i\hbar}{2m} \frac{\partial^2 \...
- 297
1
vote
1
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63
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Gaussian wave packet with complex coefficients [closed]
I am trying to obtain a representation of the momentum-space wavefunction $<p'|\alpha>$
Its position space wavefunction is given as
$$ <x'|\alpha> = N \exp [-(a+ib)x'^2 +(c+id)x'] $$
where ...
- 11
-1
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1
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Is complex integration needed when normalizing a wave function?
I have to find $\phi_0$ from following wave function in the momentum space:
\begin{equation}
\phi(k) = \phi_0 \text{exp}\bigg(-\frac{(k-k_0)^2}{2\kappa^2}\bigg)
\end{equation}
I know that I have to ...
- 109
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63
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What is an imaginary gauge potential?
This paper considers a generalised Strum-Liouville equation, that is equations of the form
$$
\left[-\frac{d}{dx}p(x)\frac{d}{dx}-\frac{i}{2}\left(\lambda_1(x)\frac{d}{dx}+\frac{d}{dx}\lambda_2(x)\...
- 121
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73
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Why is psi square a possibility? [duplicate]
Is psi square just an assumption? Or there is a physical reason why they defined like that? My procedure is:
It is intuitive for me to think possibility is proportional to energy distribution. ...
김건형
3
votes
1
answer
883
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Wave amplitude as a complex number?
In section 1-3 An experiment with waves of The Feynman Lectures on Physics (https://www.feynmanlectures.caltech.edu/III_01.html) it says:
"The instantaneous height of the water wave at the ...
- 167
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2
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64
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Absolute values when normalising the wavefunction
My question concerns Problem 1.4 from Griffiths. I understand the general working of the problem (given below), and derived the correct result for the normalisation constant $A$, but I am troubled by ...
- 187
2
votes
2
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234
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Why using real wave functions instead of complex ones?
I have already seen similar questions asked in the site (like this or this), but I don't feel that my question has been fully addressed.
I understand that orbitals $np_x$ and $np_y$ are linear ...
- 123
3
votes
1
answer
110
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How does the wavefunction transform under an arbitrary change of variables?
Suppose we have a variable $x$ and a probability density $\rho(x)$. The pushforward of this density under a bijective function $y = f(x)$ is given by
\begin{equation*}
\rho'(y) = \frac{\rho(f^{-1}(y))}...
- 858
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2
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Why is a wave function $\psi$ needed for QM? Is it possible to make a differential equation involving just the p.d.f. $|\psi|^2$ of a particle? [duplicate]
Why do you need a wave function $\psi$ for quantum mechanics? Can't you just make a differential equation involving just the p.d.f. $|\psi|^2$ of a particle? Since basically with quantum mechanics the ...
- 2,035
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Why is the formula for expected value of nonobservables in quantum mechanics different then in regular statistics? [duplicate]
Specifically, why is the operator “sandwiched in” between $\Psi^*$ and $\Psi$? i.e. Why isn’t the formula just $$\langle \hat{Q} \rangle = \int \hat{Q}\cdot|\Psi|^2 dx = \int \hat{Q}\cdot\Psi \cdot \...
- 2,327
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2
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Why is time harmonic follow the form of $e^{-i\omega t}$, not $e^{i\omega t}$? [closed]
In physics, when we solve an PDE or ODE, the solution usually has the form of
\begin{equation}
f=C_+e^{i\lambda x}+C_-e^{-i\lambda x}
\end{equation}
and the "causility" will eliminate one ...
- 19
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91
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Can I see $Ψ^∗(x,t)$ as a linear functional which can be aplied on wavefunction $\Psi(x,t)$?
Let's say I have a wavefunction $\Psi(x,t) = A e^{i(kx−ωt)}$. Now I complex conjugate it which gives me $\Psi^∗(x,t)$.
My first question is: Does $\Psi^∗(x,t)$ live in the dual of a Hilbert space?
My ...
1
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4
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Eigenvalue problem of $L_z$
From Shankar's QM book pg. 313, the eigenvalue problem for $L_z=XP_y-YP_x$ in polar coordinates is
$$-i\hbar \frac{\partial \psi(\rho,\phi)}{\partial \phi}=l_z\psi(\rho,\phi)$$
since $L_z=-i\hbar\frac{...
- 4,235
2
votes
2
answers
592
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Property of a wavefunction
We know that a wavefunction can't be completely real, because then it would have some complex expectation values for some operators. If we let $\psi$ be a real wavefunction, then
$$\langle P\rangle= \...
- 71