New answers tagged wavefunction
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The Source of Interference in the Delayed Choice Quantum Eraser
The link you posted is not accessible to the general public, but I assume you mean the Kim et.al. experiment from 1998, as described on Wikipedia.
1: Why is there a pi phase shift between the two ...
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Why isn't there a discontinuity in the derivative of the wavefunction with a finite square well?
The reason is the same as in the case of the continuity of the wave function.
In the case of piecewise continuous potential energy, in each interval of continuity of the potential, Qmechanic's ...
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Why isn't there a discontinuity in the derivative of the wavefunction with a finite square well?
Yes, that is essentially it. The continuity of the derivative $\psi^{\prime}$ follows from
the TISE $\frac{\hbar^2}{2m} \psi^{\prime\prime} = (V-E) \psi $ in integral form, and
the continuity of the ...
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How does the wavefunction transform under an arbitrary change of variables?
TL;DR: As the overall phase of the wavefunction is not physical, OP's question has a non-unique answer that ultimately comes down to a choice of convention. Within a given class of situations we often ...
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Why $n-\ell-1$ nodes?
The number of nodes has to be an integer (because the wavefunction crosses the axis an integer number of times)
let's call that integer $k$
$l$ is also an integer.
Now define $n$ as
$$
n = k + l + 1
$$...
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Why $n-\ell-1$ nodes?
There's not a whole lot of physics here. For given $\ell$, the radial part of the Schrödinger equation is equivalent to that of a one-dimensional problem, and for such a problem it is known from the ...
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What is the quantum state of a particle sitting at rest at the minimum of its classical potential?
The harmonic oscillator has Hermite functions, $\psi_n(x)$, as eigenvalues with energy $\hbar\omega(n+\frac 1 2)$. The classical minimum is:
$$ \psi(x) \propto \delta(x) $$
You can expand that into a ...
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What is the quantum state of a particle sitting at rest at the minimum of its classical potential?
The Heisenberg uncertainty principle states that the more accurately you know the position of a particle the less accurately you know it's position. This means we can never ask for the wavefunction of ...
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What is the meaning of two wavefunctions being "same"?
Two wavefunctions being same is a misleading figure of speech: what is really meant is that bosons occupy the same state. When talking about multiple indistinguishable particles, we describe them by ...
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Equation of wave motion in one direction
This is the Helmholtz equation. Unfortunately the text isn't doing you any favors by seemingly pulling it out of nowhere, and on top of that, referring to it as an "equation of wave motion", ...
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Eigenfunctions of time-independent Hamiltonians
It is not always true that eigenfunctions of self-adjoint operators form a Hilbert basis (or a complete orthonormal system if you prefer).
Before addressing this point, let me first address your ...
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Can we construct a wave function for black body radiation?
Not the wave function, but the density matrix - since we are dealing with a thermodynamic state. In fact, this density matrix is our starting point in modern description of the Black body radiation:
\...
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Eigenfunctions of time-independent Hamiltonians
A differential operator $H$ cannot act on every function in the Hilbert space because not all of them are differentiable. We can relax our notion of differentiability and permit weak derivatives, ...
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Why can't photons be localized as wavepackets like massive particles can? What specifically goes wrong in the math if we try to model them this way?
I will only make an answer about the position operator.
The most well-defined things that we may reliably say that we can measure, are Hamiltonian eigenvalues. It should be good on hindsight---you can ...
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Behavior of the temporal part of the wavefunction in an infinite well
So how does it go from a positive point to a negative point if it can never be zero?
The wavefunction is complex. At a given point it has a value of $A e^{-i E_n t/\hbar}$. So if its value at a ...
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Solution of Time Independent Schrodinger Equation
The time-independent Schrödinger equation for a free particle
(i.e. with a potential energy $U(x)=0$)
$$-\frac{\hbar^2}{2m}\frac{d^2\psi(x)}{d x^2}=E\psi(x)$$
has indeed the solutions
$$\psi(x) = Ae^{...
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Are photons actually particles at all?
Photons are different from other particles because photons are massless and hence have no meaningful non-relativistic limit as they always move at $c$. I will not rehash the various approaches to ...
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