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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Non-locality of the wavefunction in QM and Twistor theory [closed]
Regarding locality, I don't think locality is a principle per se, but we often assume that the physical fields are local on spacetime, describable by partial differential equations and so on. But of ...
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How do operators on kets and wavefunctions correspond?
Let $\hat{A}$ be an operator on Hilbert space vectors. How does one show that there always exists a corresponding operator $\hat{a}$ on wave functions? i.e. $\exists \hat{a}:L^2\rightarrow L^2$ s.t. $$...
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Physical meaning of symmetric and antisymmetric wavefunction
On describing Bosons and Fermions, the symmetry of wavefunction is introduced first. Here, If two particles a and b, are in two states n and k respectively, we get the wavefunction individually. On ...
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Dirac's Bracket Notation
I have a question on Dirac's bracket notation. In particular, according to this notation, vectors and covectors are represented by $|\psi\rangle$ and $\langle\psi|$ respectively. Moreover, these two ...
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Connection between dispersion relation and symmetries of the Hamiltonian
I am having trouble understanding intuitively the connection between the dispersion relation and the symmetries of the Hamiltonian. For example, suppose we have a lattice and there are four sub-...
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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, ...
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Calculating the expectation value of the angular momentum operator
I'm not looking for the exact answer to the question, but rather why a certain way of solving it is chosen. We agree on the answer, but why is the approach different. I'm afraid it's a sign of me not ...
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The eigenvectors associated to the continuous spectrum in Dirac formalism
I am comfused about the definition of an observable, eigenvectors and the spectrum in the physics litterature. All what I did understand from Dirac's monograph is that the state space is a complex ...
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Quantum Mechanical Current Normalisation
Consider an electron leaving a metal. The quantum-mechanical current operator, is given (Landau and Lifshitz, 1974) by
$$
j_x\left[\psi_{\mathrm{f}}\right]=\frac{\hbar i}{2 m}\left(\psi_{\mathrm{f}} \...
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Hydrogen radial equation solution's boundary condition for $r \to 0$ [duplicate]
I am studying the hydrogen atom and I am analysing the radial equation: $$\left[\frac{-\hbar^2}{2m} \frac{\partial^2}{\partial r^2} + \frac{\hbar^2l(l+1)}{2m}+ V(r)\right]u=Eu$$ with $V(r)$ equal to ...
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Phase Coherence in the BCS wavefunction and the Cooper Pair Wavefunction
I have a couple question regarding the following BCS wavefunction ($|0\rangle$ is the vacuum state):
$$|\psi\rangle = \Pi_k \big(|u_k|+|v_k|e^{i\varphi}c^\dagger_{k\uparrow} c_{-k\downarrow}\big)|0\...
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Fermions in a infinite 1D well and spinorbital
I am learning quantum chemistry. To have a comprehensive understanding of the Slater determinant, I studied the classical problem of two indistinguishable particles in a 1D box with infinite barriers. ...
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Negative kinetic energy on a step potential
I'm doing an introductory course on quantum mechanics. I'm having trouble with the explanation of the kinetic energy on the classically forbbiden region on a step potential ($V=0$ for $x<0$, $V=V_0$...
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Time derivative of complex conjugate wave function [duplicate]
We have
$$\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 \...
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What Does Feynman Mean When He Says Amplitude and Probabilities?
In Feynman lectures on gravitation section 1.4, he tries to debate over whether one should quantize the gravitation or not.
He provides a two-slit diffraction experiment with a gravity detector, which ...
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Other than approximating the total energy of the system, what other information does the Hartree-Fock method provide?
In the Hartree-Fock method, one computes the energy of an interacting quantum-many body system, described by $H$, via taking a non-interacting trial ground state, $|\psi_{\mathrm{HF}}\rangle$, and ...
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Derivation of Schrödinger equation in Feynman-Hibbs
I am going through the derivation in chapter 4-1 of "Quantum Mechanics and Path Integrals. Emended Edition" by Feynman and Hibbs. The chapter starts with a proof of the equivalence of the ...
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If a proton transforms into a neutron by releasing a positron why should this process create more mass? [duplicate]
If waves can interfere and thats why cancel out or add up why we cannot think the same about the natterial feature called mass as in this explained example in the title of this posted question??Thanks ...
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Can the Parity Operator in polar coordinates be defined as $\hat\Pi\psi(r,\theta,\phi) = \psi(r,\theta+\pi,\phi).$?
I was reading about Symmetries & Conservation Laws from Introduction to Quantum Mechanics, David J. Griffiths when I came across this question about the parity operator in three dimensions:
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Is the zero vector necessary to do quantum mechanics?
Textbook quantum mechanics describes systems as Hilbert spaces $\mathcal{H}$, states as unit vectors $\psi \in \mathcal{H}$, and observables as operators $O: \mathcal{H} \to \mathcal{H}$. Ultimately, ...
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Quantum collapse: our invention? [closed]
I'm wondering if a similar scenario has already been proposed, or if this one is somehow valid. I'm a complete layman so be patient.My reasoning goes like this: is the collapse of the wave function a ...
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Physical meaning of each term of the square modulus of a wave function
The expression below is the square modulus of the wave function of a harmonic potential ($V=\frac{1}{2}m\omega^2 x^2$) in which it's stated that the probability of finding the particle in the $\psi_0$ ...
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Has quantum measurement and particle appearance ever been modelled as a resonance effect created by the measuring device on the quantum wave?
Has anyone ever modelled quantum measurement as a resonance effect, that is created by introducing a measuring device into the quantum system?
An analogy may explain what I mean: if you take the free ...
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De Broglie wavelength and how it leads to the wave function
From what I know, de Broglie derived the wavelength equation using Einstein's $E=mc^2$ and the Einstein-Planck equation $E=h\nu$. My teacher explained this by saying an electron literally moves in ...
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Classical Hamilton’s equations in quantum mechanics [duplicate]
How can one derive what the position operator is in momentum space for a quantum wave function from the classical Hamilton’s equations?
Similarly, is a concept of an “angular momentum space” ...
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Can Hartree-Fock determinant WLOG taken to be real?
For a many-electron Hamiltonian $H$, a Hartree-Fock determinant is a Slater determinant $\Psi$ that minimizes the energy $\frac{\langle\Psi,H\Psi\rangle}{\langle\Psi,\Psi\rangle}$. In general, $\Psi$ ...
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$\pi$ phase shift upon reflection in quantum wells
Is there a similar phenomenon to the $\pi$ phase shift experienced by light upon reflection from a medium of lower to higher refracted index for particles in different potentials?
For instance, does a ...
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Why are wavefunctions not considered hidden variables?
In the proof of Bell's theorem of 1964, referenced e.g. here, the definition of a hidden variable seems to be any variable from which we can derive the correlation between the detectors, by ...
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How is Zig-zag Motion Observable in Quantum Mechanics Given Wave Function Collapse?
I'm puzzled by a concept I read about in a physics text concerning quantum measurement. The text describes the potential to observe a "zig-zag" motion if one could capture images of an ...
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Eigenstates of the Laplacian and boundary conditions
Consider the following setting. I have a box $\Omega = [0,L]^{d} \subset \mathbb{R}^{d}$, for some $L> 0$. In physics, this is usually the case in statistical mechanics or some problems in quantum ...
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