Questions tagged [wavefunction]
A complex scalar field that describes a quantum mechanical system. The square of the modulus of the wave function gives the probability of the system to be found in a particular state. DO NOT USE THIS TAG for classical waves.
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Why is the electron probability density finite at the nucleus despite the Coulomb potential being singular?
In the hydrogen atom, the Coulomb potential
$$V(r) = -\frac{e^{2}}{4\pi\varepsilon_0 r}$$
$$\psi_{1s}(0)=\frac{1}{\sqrt{\pi a_0^3}}$$
This seems contradictory: how can the electron have non-zero ...
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Is it valid to keep $k_1$ and $k_2$ when considering a light propagating along $z$ axis?
If a mode function of the light is given by $\psi_{\mathbf k}(x^\mu)=ce^{ik_\mu x^\mu}$, where the degrees of freedom of polarization are suppressed, it can be normalized by requiring $\left <\psi_{...
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Interpretation of a solution in Quantum Mechanics [closed]
I am a Math student and I am following a course in Quantum Mechanics. I am having some trouble understanding the physical solution of some problems. For example, consider the simple problem of a “...
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Noob questions about wavefunctions [closed]
I am trying to learn a little bit on my own about how we talk about physical systems on a high level of precision, partially because I'm getting into chemistry and want to understand what is ...
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Confusion in the implications of Bloch's Theorem [duplicate]
I am a beginner in condensed matter physics and I am reading Bloch's Theorem from a book by Ashcroft & Mermin. It is saying that
because the set of all wave functions and energy levels for two ...
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Reference request: Byers-Yang theorem
Recently I have become interested in learning more about Byers-Yang theorem, however I haven't been able to find many references where it is discussed in detail, other than the original 1961 paper. I'...
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Trying to understand Pauli Exclusion Principle (Griffiths)
I'm trying to learn physics on my own but I am a bit stuck on the identical particles unit in the Griffiths textbook, specifically trying to derive how the Pauli exclusion principle happens.
From the ...
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Question on Wave Function Collapse in Quantum Experiments [duplicate]
Is it really the act of conscious observation that collapses the wave function, or could it be the presence of additional measurement apparatus eliminates the interference pattern independent of a ...
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(QM) What exactly is inner product in Dirac notation?
I'm a new learner of quantum mechanics and I have some problems about inner product in Dirac notation.
By Dirac notation, a function $f(x)$ is represented by |$f$$>$ .
According to my knowledge, $&...
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Density matrix of particle on a circle
Consider a particle constrained to a ring of circumference $L$. Following this paper, the position eigenstate on a circle can be expressed in terms of the position eigenstates on the real line as
$$
\...
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Why does the wavefunction collapse after no detection?
In a beam splitter experiment with a single photon, if I place a detector on one path and after some time it never clicks, why does the wavefunction still collapse to the other path even though I ...
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Alternative Equation for QM [closed]
If we start with a plane wave
$$\Psi(x,t) = e^{-i\frac{E}{\hslash}t}e^{-i\frac{p}{\hslash}x}$$
Then we have
$$\partial_t\Psi(x,t) = -i\frac{E}{\hslash}e^{-i\frac{E}{\hslash}t}e^{-i\frac{p}{\hslash}x}
=...
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Why does squaring the operator $-i\hbar \frac{\partial}{\partial x}$ result in a second derivative?
I understand that to calculate the expectation of any value of a quantity $Q(x,p)$ we integrate $$\int\Psi^{ \ \ast}[Q(x,-i\hbar \frac{\partial}{\partial x})]\Psi dx.$$
However for expectation value ...
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Why does this condition hold for normalizable wave functions? [duplicate]
I am reading Griffiths' Introduction to Quantum Mechanics, and on Page 14 the footnote states that in 1D normalizable wave functions $\Psi(x,t)$ goes to zero faster than $\frac{1}{\sqrt{|x|}}$, as |$x$...
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Is it possible that the square amplitude law is only approximately correct?
I would like to ask about the law in quantum mechanics whereby the measured probability is the square of the probability amplitude.
Is it possible that the law is only approximately correct, i.e. it's ...
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Why do we use Hilbert Space? [duplicate]
While studying quantum mechanics, I encountered the term Hilbert Space.
As I understand, Hilbert space is an infinite-dimensional complete inner-product vector space.
What physically motivates such a ...
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Why are there two different types of visual depictions of electron orbitals?
I was refreshing myself on electron orbitals and quantum numbers. I’m seeing two different looking depictions of some of these orbitals.
the second diagram aligns more with what i’m reading on the ...
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How does quantum tunneling conserve Energy?
Picture a particle in a square well where:
\begin{align}
-\frac{\hbar^2}{2m}\nabla^2 \psi = E\psi &\qquad \text{if $|x|<L$} \\
\left ( -\frac{\hbar^2}{2m}\nabla^2 + V_0\right) \psi = E\psi &...
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How to obtain the general explicit form of the vector state and wavefunction in the case of a continuous degenerate spectrum
$\newcommand{\ket}[1]{|#1\rangle}$
I'm trying to figure out what the general form of the vector state (and wave function) look like in the case of a continuous spectrum with (for now) discrete ...
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Wave Function and Measurement (Landau-Lifschitz Volume 3)
I believe Landau is trying to motivate the collapse of a wavefunction. However, there are some parts which are confusing.
He claims that the apparatus is in an initial state $\Phi_0(\xi)$ while the ...
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Is it possible to determine whether a quantum many-body system has a bound state?
Let's say we have a quantum system of particles interacting (for simplicity) via 2-body terms, so that the Hamiltonian is
$$\hat{H} = \sum_i\frac{\mathbf{p}_i^2}{2m_i} + \sum_{(ij)} v_{ij}(r_{ij}) .$$
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Doesn't the Many Worlds Interpretation simply move the collapse of the wave-function to the brain/consciousness? [closed]
As far as I understand as a layman (and forgive me if I say anything wrong, I am merely stating my current understanding), quantum mechanics predicts outcomes based on a wave function, which is a ...
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What is wave nature of particles? [closed]
De Broglie's Hypothesis proposes wave nature for all matter in this universe and calculates the wavelength for this so called "matter-wave".
I want to know what exactly this matter wave is, ...
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Why can't a particle with definite momentum be localised in space?
I'm watching this video by Float Head Physics, which presents a narrative where the YouTuber "Mahesh" is learning about the Heisenberg uncertainty principle from Feynman (starting around 13:...
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Does QFT treat time and space on the same footing using eigenkets of space and time?
Question: As position and time are not operators in QFT (and thus eigenkets of each do not exist), how does QFT treat time and space on the same footing and how does this formulation differ from the ...
