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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Do spin wavefunctions live on a Hilbert space?

This question comes to mind while reading the quote in different books which is "Hilbert space is infinite dimensional". While the electron spin is 2 Dimensional problem. Secondly, we ...
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Parity of ground state of truncated harmonic oscillator [closed]

**Why soln for truncated oscillator exist only when wave function is zero at x=0 and the states must be odd only? How to calculate parity for ground state of truncated harmonic oscillator?** strong ...
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Clarification on calculating probabilities for a particles location (basic)

Say that we have a wave function $$\Psi(x,t)=c_1\Psi_1(x,t)+c_2\Psi_2(x,t)$$ where the particle is confined to $[0,a]$, $\Psi_i$ corresponds to the normalised wave function for energy $E_i$, and $c_i$ ...
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Bound States of a Particle in a Half-Infinite Potential Plus a Delta Function [closed]

I am having some conceptual problems regarding the bound states. I will try to address them using a simple problem. Consider a particle which is under the effect of a half-infinite potential plus a ...
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Using separation of variables to solve Schrödinger equation for a free particle

I was reading Introduction to Quantum Mechanics by David Griffiths and I am in Chapter 2, page 45. I know that since the solutions from Schrödinger equation cannot be normalized for a free particle. ...
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Can different electron orbitals within the same atom be entangled?

Could the electron in the outer shell orbital be entangled with an electron within the inner S orbit of the atom? If so, how would this affect the properties of such an atom, such as emission and ...
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Can we find the functional for a quantum field in QFT

I've heard that QFT is really described by a functional which dictates the probability that a field will be in a certain configuration $\Phi[\phi]$. My question is, can we find an equation that will ...
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What happens when a laser beam is stuck between two mirrors and the distance in-between is decreased gradually? Heisenberg Uncertainty Principle

Assuming a laser beam going back and forth between two mirrors, what would happen if we keep bring the mirrors closer and closer to each other? Because after a certain width, we would be knowing both ...
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Shifting the derivative for wavefunction [closed]

In deriving Newton's second law using quantum mechanical laws, I learned that $$ \frac{\partial^2 \psi}{\partial x^2}\frac{\partial \psi^*}{\partial x} = -\frac{\partial^2 \psi*}{\partial x^2}\frac{\...
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How does the wavefunction look like for inverted oscillator potential? [duplicate]

Suppose the inverted harmonic oscillator potential $$H=\frac{p^2}{2m}-\frac{1}{2}m\omega^2x^2$$ I'm looking for a form of solution for the case when $E<0$. It's clear that a scattering solution ...
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636 views

Why is one equation solution for the wave equation while the other isn't? [closed]

Can someone explain why the equation $$y(x, t) = A \log(x + vt)$$ is a solution for the wave equation while $$ y(x, t) = x − 2$$ isn't? I just couldn't understand my professor explanation, he said I ...
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Why is there a measurement problem? [closed]

From what I understand, the measurement problem seems to be a problem of humans limitations and nothing more. It seems to be pretty egocentric. We're saying, because we can only observe one probable ...
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Delocalized electron wavefunction for a set of finite potential wells

I have to solve a problem using MATLAB where I have to plot the wavefunctions of the electron in a set of 10 finite potential wells arranged adjacent to each other with the potential at the extreme ...
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1answer
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Entanglement and continuous basis sets

I've usually seen entanglement discussed when dealing with discrete basis sets. For example, if we consider the Hilbert space $\mathcal{H}_0\otimes\mathcal{H}_1$, where both $\mathcal{H}_j$ are two ...
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Is this proof of Griffith's watertight?

In the introductory pages of Griffith's book on Quantum Mechanics, he says: But wait a minute! Suppose I have normalized the wavefunction at time $t=0$. How do I know that it will stay normalized as ...
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1answer
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Necessary and sufficient condition for the probability current being zero in quantum theory [closed]

I am self-studying introductory quantum theory and I am stuck on a question from an undergraduate course regarding the continuity equation / probability current. For $\Psi(x,t)$ as a solution of ...
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Probability current (Integral in all space)

So , when we take the integral in all space of the probability current j (as defined in the first relationship here https://en.wikipedia.org/wiki/Probability_current) in non relativistic quantum ...
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How to rigorously prove that the toric code ground state has non-trivial topological order?

Consider the unique ground state $|\psi\rangle$ of Kitaev's toric code model on a sphere. Has it been rigorously proved that $|\psi\rangle$ cannot be transformed into a trivial product state by ANY ...
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In objective collapse theory, do large objects constantly collapse?

In objective collapse theory, do large objects constantly collapse? So I understood it like this: Wave collapses into one concentrated point, Wave spreads out, Wave collapses into one concentrated ...
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Find the eigenvalue of 1D system of three identical quantum wells

The following is the problem I need help: Consider an electron in an one-dimensional system of three identical quantum wells mounted on a substrate and separated equally by the distance r, as shown ...
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1answer
67 views

How does $\sum_k \psi_k^*(\vec{r})\psi_k(\vec{r}')=\delta(\vec{r}-\vec{r}')$ express the completeness of a basis?

The annihilation field operator is defined as $$\hat{\psi}(\vec{r})=\sum_k \hat{b}_k \psi_k(\vec{r})$$ Two of these operators satisfy the commutation relations $$[\hat{\psi}(\vec{r}),\hat{\psi}^{\...
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Is there a time component for each probable state of the wave function?

In other words, when does time or a time direction come into play or does it in the equations? Is there time or time directions associated with each probable state of a quantum system or does time ...
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Plain progressive simple harmonic wave

We know the equation of a plain progressive simple harmonic wave going from left to right is, $$y=a\sin\frac{2\pi}{\lambda}(vt−x).$$ If we put $t=0$ and $x=0$, we get $y=0$; and if we put $t=0$ and $x=...
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Wave function and uncertainty principle

Why is the position of a particle in the Schrödinger wave equation represented as an exponential periodic wave $$A\exp\left(\frac{(2\pi\iota)(px-Et)}{h}\right)$$ where $p$ is momentum and $E$ is the ...
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1answer
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Spacetime curvature around Gaussian wave packets

https://en.wikipedia.org/wiki/Wave_packet#/media/File:Wavepacket-a2k4-en.gif From quantum mechanics we know how to describe, statistically, an unbound particle floating in space. Treat it as a ...
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How to find Fourier transform of continuum state? [closed]

I am working on a problem which requires me find the projection of a plane wave onto a continuum state of a Coulomb potential. How would I go around calculating $$I = \left\langle \psi_E \middle| k \...
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The Variational Method

I'm reading about the variational method in Shankar's Principles of Quantum Mechanics, page 433. The author states that if we have the trial ket $$|\psi\rangle = |E_0\rangle + |\delta\psi\rangle$$ ...
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Wave Function Probability calculation [closed]

Redited The wave function of the particle at a certain instant is given as $$\psi(x)=Ae^{(-\frac{x^2}{a^2}+ikx)}.$$ If $P1$ and $P2$ denote the probabilities of finding the particle in the range $a$ ...
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Solutions to Schrödinger's equation in 2D polar coordinates when the potential is zero

For Schrödinger’s equation, in polar coordinates $(r, \theta)$, when the potential in the Hamiltonian is $0$ (free particle), I think a solution is $r^{-1} e^{-i(kr - \omega t)}$. This radial wave is ...
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The normalization of the momentum eigenfunction [duplicate]

If the momentum eigenfunction is this but it is not normalized, and if we apply the normalization condition which is this will you get infinity instead of 1?
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De Broglie wavelength of large objects [duplicate]

I've seen some examples/problems where the de Broglie wavelength of large objects (like a tennis ball) is calculated and this doesn't really make sense to me. So the baseball consists of many smaller ...
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1answer
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Two electrons in the ground state

I've been introduced to multiple particle systems in quantum mechanics, and in the case of the $2$-electron system, I'm facing this massive confusion. In the ground state of a $2$-electron system, you ...
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Does the Fourier transform apply for any number of dimensions?

I've seen the equation to get from the momentum wavefunction to the position wavefunction as $$\Psi(x)=\frac{1}{\sqrt{2{\hbar}\pi}}\int_{-\infty}^\infty{e^{ipx/\hbar}}\Phi(p)dp$$ I was wondering if ...
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Completeness of Landau basis

We know that the Landau Hamiltonian (uniform magnetic field) is diagonalized by wavefunctions $|n,m\rangle,n,m\in \mathbb{N}$ in the symmetric gauge. However, does this set of functions form a "...
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How to predict the photoelectric effect with modern quantum theory?

In introduction class to quantum mechanics, the example of the photoelectric effect is often shown to the students to explain how the classical physics fails to explain it. We are told that one can ...
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Would a non-separable position momentum wavefunction really violate the uncertainty principle? [closed]

I've seen it claimed on here that a position momentum wavefunction would violate the uncertainty principle. I would interpret as saying that position momentum wavefunctions that are not separable ...
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In FQHE, can we derive the Hamiltonian from Moore Read wave function?

I am wondering since we cannot derive the wavefunction from Hamiltonian in the Fractional Quantum Hall Effect, can we derive the Hamiltonian from the wavefunction? What will the Hamiltonian look like? ...
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Wave-Particle Duality and Quantum Wave Functions & States?

Apparently Quantum object have wave-particle duality as their property: electron is like a wavelet in macroscopic level. Also when it's orbiting an atom: it must form a standing wave (de Broglie). ...
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Do we use both real and imaginary part of the wave function in quantum mechanics as opposed to classical mechanics?

In classical mechanics and physics, it's typically said that when we write a wave as $\Psi(x,t)=Ae^{I(kx+\omega t+\delta)}$, what we mean is to take only its real part; that is, $\Psi(x,t)=\Re\left\{...
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Probability distribution function of the photon's scattering angle

What is the normalized probability distribution function of the photon's scattering angle, $\theta$, in Compton scattering effect when a photon hits an electron?
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What is meant by the localization of a wave function?

Shannon entropy, in terms of position space wave functions, can be written as, \begin{equation} S= -\int^{\infty}_{-\infty} \vert \psi(x) \vert^2 \log \vert \psi(x) \vert^2 dx. \end{equation} In ...
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Why do we need the radial probability distribution function?

I know that the radial probability distribution function gives us the probability of finding an electron between in a spherical shell of thickness $dr$ which is at a distance $r$ from the nucleus. Now ...
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Pauli Exclusion Principle Violation, Why is Energy Quantized?

The orbitals of an atom can be thought of as being formed from the probability of finding electrons in those orbitals. If the orbital is 1s (n = 1, l = 0), then it has a certain "volume" for ...
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What is the intuition behind density matrix?

What gives density matrix the expressive power to be able to represent mixture of pure states? For example if $|\Omega\rangle$ is 50-50 mixture of $|\Psi\rangle=\frac{1}{\sqrt{2}}(|u\rangle+|d\rangle)$...
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What is the Schrödinger equation in position velocity space?

One way I've seen the Schrödinger equation expressed for the position wave function is $$\frac{i\hbar\partial\Psi\left(\vec{r},t\right)}{\partial{t}}=-\frac{\hbar^2}{2m}\nabla^2\Psi\left(\vec{r},t\...
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What determines whether two quantum particles will "interact?"

The concept of quantum particles interacting is confusing to me. By "interact" I mean that thing particles do where they become entangled and exchange information and wavefunction collapse ...
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Do any real quantum measurements resemble this measurement model?

There's this simple model of measurement that I've seen in several books and papers (Peres's, Von Neumann's, Bell's, Bohm's, etc.). We have a system to be measured with coordinates $q,p$ and a ...
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Time-dependent quantum mechanics and state space [duplicate]

I apologize if this question ends up being too basic, but I couldn't find the answer by myself and I'm sure you can help me. In quantum mechanics, one takes a complex Hilbert space $\mathscr{H}$ as ...
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1answer
86 views

What is the difference between anti-symmetric wavefunction and asymmetric wavefunction?

In section 8.2.4, Zettili, in his book Quantum Mechanics, explains how we can construct symmetric and anti-symmetric wavefunctions using asymmetric wavefunction. Although he explains that symmetric ...
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How to calculate the amplitude of two degenerate vacuums?

I've seen in textbooks and heard from lecturers that spontaneous symmetry breaking (SSB) does not happen in quantum mechanics because of the tunnelling between two degenerate vacua (i.e amplitude of ...

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