All Questions
Tagged with wavefunction superposition
107
questions
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Do Helium-4 atoms behave like photons?
I know that the Helium-4 atom is a boson. Does this mean that, like photons, many Helium-4 atoms can be placed at the same point in space?
How its possible? It includes fermions (Protons, Neutrons, ...
- 209
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80
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Amplitude superposition for different kinds of particles
We have seen that the probability of finding a particle at a particular point is the square of its wave function. In the double slit experiment, we notice that wave functions add up and the resultant ...
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A simple question in quanum mechanics on position and momenum eigenstates
The eigenfunctions (eigenstates) for the momentum of a particle are given by the plane waves
$$\phi(x,t) = \sin(kx - \omega t)$$
If we sum a large number of these waves in a range from $0$ to $k_m$, ...
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Semi-classical Quantum Ping-Pong in an infinite well potential
The general one particle state in a simple infinite well of size $L$ is a superposition of all the Hamiltonian eigen-states:
$$\tag{1}
\psi(x, t) = \sqrt{\frac{2}{L}} \sum_{n = 1}^{\infty} c_n \, e^{-\...
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Can other objects feeling the gravitational effect of a particle that is in a state of superposition cause its wavefunction to collapse? [duplicate]
When I feel the slight gravitational pull of one particle that is in a state of superposition and I measure the exact pull at any given instant does the wavefunction collapse? If particle A constantly ...
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80
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Can two normal 1D waves form a wave packet?
I have a confusion
A wave packet is described by the superposition of two wave functions: $$Ψ_1(x,t)=A\sin(k_1x−ω_1t)$$ and $$Ψ_2(x,t)=A\sin(k_2x−ω_2t),$$ where $k_1=2.0×10^6\text{m}^{−1}$, $k_2=3.0×...
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Circular wave superposition
(Per title, I do mean circular wave, not radial wave.) I'm trying to learn about wave mechanics through some 3D simulations, and I've arrived at an interesting case that I can't seem to answer through ...
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65
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Why discarding the linear combination of solutions?
In Griffiths's textbook (Introduction to quantum mechanics), part I, 4.1.2, he's solving Schrodinger equation in three dimensions, after separating the variables $Y(\theta, \phi) = \Theta(\theta)\Phi(\...
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Understanding the potential step for a particle in 1D
In an exercise, I consider a particle moving from $x=-\infty$ towards a potential step, where $V(x)=0$ for $x\leq 0$ and $V(x)=V_0$ for $x>0$.
If we consider the case of $0<E<V_0$, we have;
$$...
- 461
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586
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How to check that any linear combination of solutions is itself a solution to the time-dependent Schrödinger equation?
David Griffiths states in 'Introduction to Quantum Mechanics':
The general solution is a linear combination of separable solutions. As we're about to discover, the time-independent Schroedinger ...
- 461
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Are energy eigenfunctions of a particle in one dimensional box orthogonal to each other?
For a particle in one dimensional box, its State Ψ(t=0) is defined as:
$Ψ= \frac{3}{5}Φ_1(x)+\frac{4}{5}Φ_3(x)$
I want to find out $|Ψ(0)|^2$.
My question is that as energy eigenfunctions $Φ_1(x)$ and ...
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120
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Why is a combination of stationary states not stationary, given the actual probability does seem to be so?
EDIT: So I thought about it and I found a trivial mistake, the eigenstates are only orthogonal over either all space or some specific interval (for example in an infinite square well), meaning that ...
- 1,775
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Why does superposing an infinite number of waves of different wavenumbers eliminate periodicity and may sometimes result in a localised wave?
I am studying how wave packets are defined in quantum mechanics, but I am finding it hard to intuitively understand why superposing an infinite number of waves of different wavenumbers $k$ may ...
- 390
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How much does the collapse of the wave function reveal about the state of the quantum prior to collapse?
The best way I can pose this question is through an example: suppose a photon passes through a beamsplitter, putting the photon into a superposition of the two paths (reflected or passed through), and ...
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In slit experiment: is it one wave function before and two wave functions after the split?
Forgive my round-about background to the question: I'm curious how the experiment "fires electrons slowly that interact with themselves"... I'm thinking that's just a simplification?
I feel ...
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