All Questions
Tagged with wavefunction time-evolution
104
questions
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2
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83
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Why is the time derivative of the wavefunction proportional to a linear operator on it? [closed]
I am currently trying to self-study quantum mechanics. From what I have read, it is said that knowing the wave function at some instant determines its behavior at all feature instants, I came across ...
- 23
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3
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209
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Basic doubt in quantum mechanics
Do entities like electrons, which are considered point particles in Classical Mechanics, actually have a definite position at a particular time (irrespective of it can be measured or not)?
- 426
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109
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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 $$\psi_{t_{2}}(x) =...
- 111
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34
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Homogeneity of Schroedinger equation implies norm conservation
I am trying to understand how homogeneity of Schroedinger equation implies norm conservation. I know that we are considering the non-relativistic case, where particle number is conserved, so we do not ...
- 1,398
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49
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Time evolution of monitored quantum dynamics
Let us assume that the quantum system consists of Hilbert space $H$ with basis vectors $|i\rangle$. The initial state $|\Psi(0)\rangle$ evolves in discrete time steps such that $|\Psi(t+\delta t) \...
- 11.9k
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72
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How we construct the Gaussian wave packet at $t=0$ with given avarage coordinate and momentum? Does it satisfy any Schrödinger equation? [duplicate]
I've begun delving into quantum mechanics and encountered a point of confusion. In classical mechanics, we define an initial position and initial momentum, which can take on any values. However, in ...
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1
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198
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Gaussian wave packet time evolution
I am currently studying quantum mechanics and I am struggling to obtain the time evolution of a Gaussian wave packet.
We know that the wave function of a free particle is:
$$\Psi(x,t)=\frac{\sqrt{a}}{(...
- 81
-1
votes
2
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79
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Cohen Quantum Mechanics Derivation? [closed]
I dont understand the argument on page 38 eq. (C-6) of Cohen's quantum mechanics. Could someone break down for me what is $g(k)$? Is it the initial condition?
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195
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The spreading of the wave function and Causality violation
In Hegerfeldt, 1998 paper "Instantaneous Spreading and Einstein Causality in
Quantum Theory" he states that,
"In nonrelativistic quantum mechanics the immediate spreading of wave ...
0
votes
1
answer
52
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Behavior of the temporal part of the wavefunction in an infinite well
I have a question about the behavior of the temporal part of the wavefunction in an infinite well. For reference, the solution given in my textbook for the wavefunction of a particle in an infinite ...
3
votes
2
answers
196
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Free particle propagator, wavefunction not moving problem
I'm learning the QM propagator and the first example is of course the free particle: $\hat{H}=\frac{p^2}{2m}$, then the new wavefunction is found by:
$$\psi(x,t)=\int dx_0\;K(x,t;x_0,t_0)\;\psi(x_0,...
- 159
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28
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Time evolution of Gaussian wave packet in free space with initial condition Dirac delta function [duplicate]
I learn something about the Time evolution of Gaussian wave packet in free space.
if the initial condition is a Dirac delta function at $t=0$, then the wave function is
$$
\psi (x,t)=\frac{1}{\sqrt{2\...
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1
vote
1
answer
119
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Can in Quantum mechanics there ever exist a 'Wavefunction' which is completely independent of time?
In Quantum mechanics the Time Dependent Schrodinger Equation tells us:
$$-\frac{\hbar ^2}{2m} \frac{\partial^2\psi}{\partial x^2} + V\psi = i\hbar \frac{\partial \psi }{\partial t }.$$
Then if any ...
- 71
1
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1
answer
265
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"Stationary" vs. moving wave packet
I am working through a quantum mechanics problem involving the time evolution of a free particle (the particle is a proton) given that the initial state is a Gaussian wave packet of the form:
$$
\psi(...
- 43
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votes
1
answer
73
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Expressing a state in Schrödinger picture and time evolution operator
I have two question, regarding the derivation of two expression that I will post below:
If we have $\{ |\phi_{n,\tau}\rangle\}$ the set of eigenvectors of the Hamiltonian of a system. This set, is at ...
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