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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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Finding normalization constant of a wave function with definite momentum

I try to read Sakurai's Modern Quantum Mechanics but I stuck at this point, $$\delta(x^{'}-x^{''})=|N|^{2}\int dp^{'}\exp\Biggl({ip^{'}(x^{'}-x^{''})2\pi\over h}\Biggr)$$ This is an expression for ...
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Using the Slater determinant to find the associated antisymmetric wavefunction

My lecture notes read: If there is one electron in the ground state, one in the first excited state, and one in the second excited state, why can we not instantly assume then, that: $$\phi_{n_i}(x_j)...
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1answer
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What is wavelength at classical turning points using WKB Approximation?

According to what I know is that a classical turning point in Newtonian Mechanics is a point where a particle has a zero kinetic energy(Total energy is equal to potential energy) and must be ...
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Get the action from knowledge of all wave functions?

Say I know all the values of the wave functions at all times $\psi[\phi,t)$. Can I use this knowledge to find the action $S[\phi]$? i.e. to give the action as a function of the wave functions? $\phi$ ...
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Symmetric potential well different solutions

I have solved $H|\psi\rangle=E_{n}|\psi\rangle$ with $V(x)=0$ from $-a<x<a$ and $\infty$ otherwise. If I propose a solution of the form $\psi(x)=A_{n}e^{ikx}+B_{n}e^{-ikx}$ I arrive to the ...
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Doubt from Momentum operator in the position basis [duplicate]

J.J Sakurai shows in the section of ' Momentum operator in the position basis' as $$P \lvert\alpha\rangle = \int dx^{'}\lvert\ x{'}\rangle\Bigl(-i{h\over 2\pi} {\partial\over\partial x} \langle\ x{...
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Get the transition amplitudes from a wavefunction?

Given a wavefunction $\psi(x,t)$ a transition from time $t_1$ to $t_2$ might be written: $$\psi(x,t_1) = \int \Delta(x,y,t_1-t_2) \psi(y,t_2) d^3y.$$ But can we solve this to get $\Delta$ in terms ...
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In the pilot-wave theory, is the quantum potential moving electrons randomly inside atoms?

As we know, in the pilot-wave theory (Bohmian mechanics), particles are guided on certain trajectories by the wavefunction. Here (In Bohmian mechanics, do electrons move inside an atom?) I asked about ...
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1answer
51 views

What is Wave Function? [duplicate]

Well, what is the meaning of wave function? What does it represent? In Schrodinger's equation, we find the value of Ψ. But what is Ψ exactly? Max Born only gave an explanation of what $Ψ^2$ (the ...
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Paraxial approximation - time varying

I want to reproduce the results of a paper I am reading. In the paper, authors use paraxial approximation. My question is: in the potential V, I can put a time dependence of space? Or the paraxial ...
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Is this a good clock for quantum cosmology?

I was thinking about Quantum Cosmology and the wave function of the universe $\Psi[g,\phi]$ in the no boundary proposal. I was thinking about what would make a good clock. It would be some function ...
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64 views

Is this explanation for the uncertainty principle correct?

In a pre-print I read that "The position of the particle is indeterminate as it could be anywhere along the wave packet. Hence compressing the wave packet to reduce the indeterminacy in position will ...
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4answers
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Does $j=\rho v$ hold in quantum mechanics?

Let's consider the current of probablity $\vec{J}(\vec{x},t)$ associated to a particle of mass $m$ with wave function $\psi(\vec{x},t)$, given by $$\vec{J}(\vec{x},t)=\frac{i\hbar}{2m}(\psi \nabla\...
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431 views

Does gravity affect the time evolution of a QM wave function?

We know that the Schrödinger equation describes the time evolution of a wave function, but how does gravity affect that evolution? For example, does the wave spread slower in a strong gravitational ...
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165 views

Are bubble chamber tracks inconsistent with quantum mechanics?

I am reading the book How Is Quantum Field Theory Possible? by Sunny Auyang, and he raises an interesting point in chapter 4 (p. 23): L. E. Ballentine argued that the projection postulate leads to ...
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Is the scalar product also a wave function?

I am wondering about the meaning of the scalar product and its relation with the wave function. In the Hilbert space, the scalar product is defined as $$\langle \phi \rvert \psi \rangle = \int \phi^*\...
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694 views

Do atomic orbitals “pulse” in time?

I understand that atomic orbitals are solutions to the time-independent Schrödinger equation, and that they are are analogous to standing waves ("stationary states"). However, even a standing ...
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1answer
49 views

Schrödinger equation in unknown potential well [closed]

Have a question from my class which I'm struggling with. We have a particle $m$ with wavefunction $φ=Ax \exp(-ax)$ when $x≥0$, and $φ=0$ otherwise. We are asked to show that the double derivative $...
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1answer
58 views

Why do quantum tunneling consume energy, if not then why it must pay back borrowed energy quickly? [duplicate]

I understand that quantum tunneling is a pure example of the uncertainty principle but clearly transistor had to be powered to work properly, anyhow I like to know if it is true that particle must ...
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55 views

Orthogonalizing a Gaussian Basis

Given a discrete Gaussian basis $$G = \{\lvert n\rangle, n \in \mathbb{Z}\},$$ where $$\langle x\rvert n \rangle = \exp\left(\dfrac{-(x-nL)^2}{2}\right),$$ with $L$ fixed. Does there exist a set of ...
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Why wavefunction becomes exponentially smaller during quantum tunneling?

I am interested in quantum tunneling and I am wondering why the wavefunction of a particle would becomes smaller so that there is a slight possibility of finding it at the other side of a big energy ...
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In Bohmian mechanics, it the uncertainty due to non-locality?

In the pilot-wave interpretation of quantum mechanics, each particle is driven by the pilot wave on the universal configuration space, and therefore its trajectory is determined nonlocally, and ...
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Why does the electron wavefunction not collapse within atoms at room temperature in gas, liquids or solids due to decoherence?

Decoherence theory predicts that any quantum particle coupled to any "large" environment should undergo decoherence and its wavefunction should collapse. This explains why measurement leads to ...
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Shape of orbitals in atoms with multiple electrons

I found this statement when browsing the Wikipedia article for atomic orbitals: "Orbitals of multi-electron atoms are qualitatively similar to those of hydrogen." Is this true? Googling around I ...
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1answer
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Wave packet in dispersive medium, how will the group velocity be affected? [closed]

A wave packet with center frequency ω is propagating in dispersive medium with phase velocity of 1.5 x 10^3 m/s. When the frequency ω is increased by 2%, the phase velocity is found to decrease by 3%. ...
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37 views

Why don't we normalize the wavefunction in time? [duplicate]

I am aware that because a particle whose wavefunction we are dealing with must be found somewhere, we normalize the probability density in position. Why do we not normalize the wavefunction in time? ...
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23 views

QM: Local phase shift in wave function

Local phase invariance ultimately lead to charge conservation but When does a local phase shift occur in a wave function?
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Wave antiparticle duality

Can an antiparticle such as the antiparticle of an electron - a positron exhbit wave particle duality. We know from de Broglie, and the Davisson-Germer experiment in which we fire electrons from an ...
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3answers
129 views

In Bohmian mechanics, do electrons move inside an atom?

Look at http://www.bohmian-mechanics.net/whatisbm_pictures_hydrogen.html. It is mentioned that in the rest states of a bound electron, the position of the electron is stationary, since the ...
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1answer
46 views

Do QED effects make a huge change to the position of the electrons?

In https://en.wikipedia.org/wiki/Lamb_shift about the lamb shift, it's mentioned that the change in the electron's frequency due to QED effects (vacuum polarization and self-energy correction) is ...
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1answer
50 views

Should physical solution to Schrödinger eq. always be real in one dimencional space? [duplicate]

one dimensional Schrödinger equation: $$ \left[-\frac{\hbar^{2}}{2 m}\frac{\partial^2\psi(x)}{\partial{x}^2} +V(x)\right] \psi(x)=E \psi(x)$$ I know that to calculate the eigenfunctions $ \psi(x) $ ...
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Can one add a discrete set of functions to complete the bound states of the hydrogen atom?

Though being an infinite orthonormal set of functions, the bound states $\Psi_{nlm}$ of the hydrogen atom do not form a basis of the Hilbert space $L^2(\mathbb{R}^3)$ due to the continuous spectrum, i....
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Wave function. Measurement of the absence

Imagine we have a particle in an eigenstate of a Hamiltonian, as time passes it will remain in that state. We suppose in this question that the position can take a continuum of values. If we measure ...
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1answer
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Feynman's derivation of Schrödinger equation. Potential spatial dependence

I am working on the book "Quantum Mechanics and Path Integrals" from Feynman and Hibbs. When finding the correspondence with Schrödinger equation he takes $$\eqalign{&\psi(x,t+\epsilon) = {}\...
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Some quantum-mechanical questions [closed]

I have recently started studying quantum mechanics, and here are some things that are really confusing me. Particle in a box: Supposedly, the square of the magnitude of the normalized wave function ...
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Stability condition of a finite difference algorithm

While studying finite difference methods of TDSE I found myself stuck on a reasoning step: The largest possible spatial curvature for the wave function, $\frac{\partial^{2}}{\partial x^{2}} \Psi(x, ...
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How much of a wave function must reside inside event horizon for it to be consumed by the black hole?

Related to this question in astronomy SE (https://astronomy.stackexchange.com/q/30611/10813) and in particular my attempt to answer it, I started to wonder which fraction of a waveform (for eg a ...
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1answer
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Wave-packet backwards emission

I am trying to reproduce the results of a TDSE two wave-packet algorithm described in "Computational Physics: Problem Solving with Python" by Landau, Paez and Bordeianu, in section 22.4 (Wave Packet–...
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Dot product of small perturbation of wave function

I have problem with this when I am doing my assignment. ∇(Ψ+δΨ)⋅∇(Ψ+δΨ) Can anyone help me explain this and how to get the expansion? Thank you.
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Solution to two non-coupled quantum harmonic oscillators

Given the following Hamiltonian: $$\hat H = -\frac{\hbar^2}{2m}\frac{\partial^2}{\partial x_1^2} -\frac{\hbar^2}{2m}\frac{\partial^2}{\partial x_2^2} + \frac{1}{2}m\omega_1^2x_1^2 + \frac{1}{2}m\...
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1answer
38 views

Mean kinetic energy without full laplacian [closed]

I need to calculate by solving the integrals the expectation value of the kinetic energy $\hat{T}$ and potential energy $\hat{V}$ operators in the state $\Psi$, defined as $$ \Psi(r) = \sqrt{\frac{1}{\...
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1answer
71 views

In QM does the observer really perturb the system to make a measurement?

It is commonly taught in introductory QM courses that in order to get to know the position or momentum of a particle, be it by "sending a photon" or similar experiments, the measurement necessarily ...
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Why can an inner product of an eigenvector also be used as an eigenvector?

In quote box below, there is an inner product of an angular momentum eigenvector. Why can you use this inner product as a new eigenvector for the next part of the work? And why do they "of course" ...
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1answer
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Interpretation of the wave function in newtonian spacetime

A Newtonian spacetime is a quintuple $(M, \mathcal{O}, \mathcal{A}, \nabla, t)$ where $(M, \mathcal{O}, \mathcal{A}, \nabla)$ is a 4 dimensional differentiable manifold with a torsion free connection, ...
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Wavefunction collapse in Stern-Gerlach experiment

Consider silver atoms coming from an S(X) apparatus, after S(X) apparatus we place an S(Z) apparatus $$ |\mathrm{SX+}\rangle= \frac{1}{2}|\mathrm{SZ+}\rangle + \frac{1}{2}|\mathrm{SZ-}\rangle, $$ ...
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Wave function collapse and a general wave function

Action of an operator on a state vector collapses the wave function to any of the eigenstate of that operator , So we get resulting state of the system as some base ket. But mathematically action of ...
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1answer
50 views

Domain of the infinite square well hamiltonian

I am reading the book by Gitman et al. 'self-adjoint extensions in quantum mechanics'. In the book, they give a precise definition of the domain of the hamiltonian of an infinite square well. For ...
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1answer
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Derivation of gradient of the expectation of local energy

Background: In Variational Monte Carlo, given a Hamiltonian $H$ and a wave function $\psi_\alpha$ dependent on some parameter(s) $\alpha$, we have defined a quantity known as the local energy, $$E_L =...
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1answer
64 views

How does the collision between two atoms work?

Considering the quantum mechanical model for an atom, what exactly happens when two atoms (say, two Ca2+ ions in a Brownian motion) collide with each other? As I know, this collision is not like a ...
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3answers
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Why can many distinguishable particles be in the same quantum state?

In Boltzmann distribution, it says we have no restrictions on how many particles there are in a same quantum state. BUT the contradiction is: Distinguishable particles mean we think their wave ...