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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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Why is the wave-function defined in abstract configuration space, as opposed to real space $\mathbb{R}^3$?

I've just began studying QM so I apologise in advance if this question is silly or badly put. My initial understanding of the wave-function $\psi(x,t)$ was that it exists in real 3-dimensional space $...
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What is “quantized momentum transfer”, and can it account for the double-slit experiment?

In https://www.sciencedirect.com/science/article/pii/S0378437109010401, the author claims that the interference pattern obtained in the double-slit experiment does not need a wave description of ...
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Density of states analogue in non-interacting multi-electron atom

I'm reading a paper on optical effects which very early on assumes that there are no interactions. Given that I want to simulate an atomic vapour (modeled, initially, at least, as non-interacting ...
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Diffraction at the everyday scale [on hold]

I know that the reason the wave like nature of matter isnt observerable at the everyday scale is because of how small planck's constant is. But if it were larger, say of the order of $10^2$ such that ...
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What is the simplest possible Hamiltonian that yields an Antisymmetric Wavefunction?

I am using a Split-Operator Fourier Transform (SOFT) technique to solve the time-dependent electronic Schrödinger Equation (TDSE) for a Hydrogen molecule under the Born-Oppenheimer approximation. So I ...
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Why do atoms repel when they are very close to each other? [duplicate]

Why do atoms repel when they are very close to each other? I know that this is not because of electrostatic force, but I do not know why atoms actually repel? Our lecturer said that it arises from the ...
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The form of the wave function in time-dependent perturbation theory

I'm trying to understand why the wave function is expressed as follows in a time dependent perturbation. I understand that since the $c(t)$ are unspecified functions, it is mathematically reasonable ...
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Why do nodes exist in wavefuncions of electrons? [duplicate]

Nodes are points in space around a nucleus where the probability of finding an electron is zero. However, is there a reason for the existence of Nodes? I'm looking for an intuitive explanation if ...
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How does Ehrenfest's theorem apply to the quantum harmonic oscillator?

Ehrenfest's theorem, to my level of understanding, says that expectation values for quantum mechanical observables obey their Newtonian mechanics counterparts, which means that we can use newton's ...
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Calculating the spin given the baryon wave function

This is probably a trivial question and I am missing something conceptually simple here. I have the spin part of the total wave function of a baryon consisting of three light quarks: \begin{equation}...
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Why do we assume wavefunctions to be finite and continuous everywhere? [duplicate]

Why do we assume the wavefunctions to be everywhere finite and continuous? Finiteness maybe required due to square integrability but why continuous? Such a restriction is not imposed on its derivative....
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If one puts a delta-function spike inside an infinite square well, is the resulting potential analytically solvable?

It was recently floated in chat that a particle in a box with a delta-function spike inside it, with hamiltonian $$ H = -\frac{\hbar^2}{2m} \frac{\partial^2}{\partial x^2} + V_0\delta(x-a) $$ and with ...
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Confused about linearity of wave equation

Currently in a QM class. My understanding is as follows: the schrodinger equation specifies solutions to your system. When we solve it we get a set of wave functions, which form a basis over the ...
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Why is $\psi_{atom}=\psi_a\psi_b$ not a suitable wavefunction for the Helium atom?

In the approximation that the two electrons of the He atom moved independently of each other, we can say that electron 1 is in state $\psi_a(1)$ where $a$ represents the orbital quantum numbers $nlm$ ...
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Expressing position wave function in momentum space for a single state

I am doing an introductory quantum mechanics course, I have been told that the momentum space wave function is essentially the Fourier transform of the position-space wave function. I.e. $$ \Phi(p,t)=\...
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58 views

What is the meaning of the notation $\langle a_1, \ldots, a_n \mid X_i(u) \mid a_1', \ldots, a_n' \rangle$? [closed]

I am from the math department and reading Belavin & Gebner's On the Algebraic Approach to Solvable Lattice Models. I am trying to understand the left-hand side of Equation (2.2) on page 4. What ...
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Does measurement of momentum always collapse the wave function into a plane wave?

When you measure $\vec p$ the wave function collapses to an eigenstate of the momentum operator. These eigenfunctions are always plane waves, correct? Does it mean that momentum always collapses into ...
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Representation of operators and wavefunctions as matrices and vectors

I remember reading somewhere that in quantum mechanics you can always set up your Hilbert space to be finite or countably infinite. However, I don't see how it's possible to to that we want to ...
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2answers
62 views

Wavefunction Basis Formalism

If we have two electrons and two possible states $| 1 \rangle$ and $| 2 \rangle$, a possible state, as I understand, could be $\frac{1}{\sqrt{2}}(| 1 \rangle | 2 \rangle - | 2 \rangle| 1\rangle)$. ...
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Why doesn't there exist a wave function for a photon whereas it exists for an electron?

A photon is an excitation or a particle created in the electromagnetic field whereas an electron is an excitation or a particle created in the "electron" field, according to second-quantization. ...
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Conceptual understanding of the Quantum Harmonic oscillator

First: When we consider a quantum particle in a harmonic (quadratic) potential we say that this particle is a harmonic oscillator, because it behaves like one. Is this correct? Now let us assume our ...
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Does Quantum Entanglement happen between two wavefunctions? [closed]

Does the entanglement happen between two particles or two wavefunctions? If it's wavefunction then what happens to the two wavefuntions after getting entangled?
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$\delta$ potential has highest probability for highest potential

I can't understand this intuitively. Figure 2.9 in Griffith's QM says that the wavefunction at $x=0$ for a delta function potential is $\sqrt{\kappa}$, and to the right it decays like $\psi_+=\sqrt{\...
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$sp^3$ Hybridization wavefunctions and probability density

I have plotted a hydrogen-like sp3-hybrid orbital probability density and it looks like this: I can plot 4 overlapping probability densities in a tetrahedral shape: So far it looks OK. But when I'm ...
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'Show that $E$ must exceed $V(x)$ for every normalisable solution of the TISE'. Surely you can show that this isn't true using exponentials?

In Griffith's this is a question, there's the clear answer which jumps out immediately: $$\frac{d^2\psi}{dx^2} = \frac{2m}{\hbar^2}(V(x)-E)\psi.$$ That is, if E is less than V the second deriviative ...
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Reality, locality, and universality in the EPR paradox

Apologies if this has been asked before. I did some searching but didn't see it anywhere asked quite like this. Thanks in advance for any insights. Caveat: I am an organic chemist and thus ...
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1answer
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How wave functions overlap in STM

In STM(Scanning Tunnelling Microscopy), as distance between tip and sample decrease tunnelling current increases. I know that when it cross barrier wave function decay exponentially. Measured current ...
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1D Infinite Square Well: Box Suddenly Increase in Size. Why the coefficients can be derived by inner producting the wave functions?

I have read the question 1D Infinite Square Well: Box Suddenly Increase in Size. How treat this?. There are two key equations in the selected answer. $$\int_0^{2L} dx \ \psi^*_m\left(x\right) \Psi\...
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What's the intuitive interpretation of quantum uncertainty $\Delta \hat{A}=\sqrt{\langle\hat{A}^2\rangle-\langle\hat{A}\rangle^2}$?

As per this video, if $\hat{A}$ is a quantum operator, the uncertainty is given by $$\Delta \hat{A}=\sqrt{\langle\hat{A}^2\rangle-\langle\hat{A}\rangle^2}$$ I understand what this expression means ...
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QM limit of QFT in Schwartz [duplicate]

In Matthew Schwartz's QFT text, he derives the Schrodinger Equation in the low-energy limit. I got lost on one of the steps. First he mentions that $$ \Psi (x) = <x| \Psi>,\tag{2.83}$$ ...
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Momentum uncertainty for a free particle [closed]

Free particle is in state psi k, where k is the wavenumber. Now i am trying to findout uncertainty in its momentum. I know that for free particle position is uncertain (delta x approaches to infinity) ...
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Why we don't need to normalize the scattering states?

I am new to QM, have find some wavefunction in different potentials, but there we need to normalize the wave function, for a reason that - particle should be found somewhere . So a wave-function, to ...
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3answers
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Can quantum randomness be somehow explained by classical uncertainty? [closed]

In quantum mechanics, the outcome of each measurement is random, distributed according to the squared amplitude of the wave function obtained from the Schrodinger's equation. Now, can someone suggest ...
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Continuity of wave function derivative

A particle is defined by a wave function, $Be^{-2x}$ for $x<0$ and $Ce^{4x}$ for $x>0$. For the wave function to be continuous at $x=0$, $B=C$. A wave function must be continuous for it to be ...
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Can Quantum Mechanical Potential have a Probability Distribution

I am currently in my second semester of undergraduate quantum mechanics. We have recently starting discussing two particle systems, usually in relation to spin interactions. In all of our calculations,...
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Approximating ground-state energy without using variational principle

Given the Hamiltonian for one dimension harmonic oscillator: $$H=-\frac{\hbar^2}{2\mu}\frac{d^2}{dx^2}+\frac{\mu\omega}{2}x^2 ,$$ I need to calculate the approximate ground state energy using the ...
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Can an electron of an atom be found anywhere? Does it need energy to happen? [closed]

According to quantum mechanics it should be possible. But can it happens when it has so small probability to occur? also if it can happens that means that energy must be provided in order to the ...
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Probability of WaveFunction [closed]

A particle is confined in a one dimensional box of length $a$. What is the probability of finding the particle at $x = a/4$? I know that the wave function is written as $$y= A\sin([(\pi x)/a]$$...
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Dependence of wave function with time, especially probability density function. And Continuity equation

I was learning Basic Quantum mechanics. I cam across the fluid equation in QM, which suggests $\Psi^*\Psi$ is probability density function. Consider the two statements below Probability will change ...
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69 views

Trying to first understand position and momentum bases in Quantum Mechanics

In my lectures, I am told: $$\langle x \mid \psi \rangle = \psi (x)$$ Which can only be valid if the overlap integral is: $$\langle x \mid \psi \rangle = \int_{-\infty}^{\infty} \delta (x-x') \ \...
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199 views

Can we derive Schrödinger equation from classical wave equation?

In classical mechanics wave equation is $$y=A\sin(kx-\omega t)$$ $y$=instantaneous displacement, $A$=maximum displacement, $\omega$=angular velocity, $x$=position of particle, $k$=wave number Now in ...
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In a spherically symmetric central potential why do we look for eigenfunctions of the angular momentum operator?

In finding the solutions to the wave equation for a spherically symmetric potential $V(r)$, we look for the eigenfunctions of $\hat L^2$ and $\hat L_z$ operators. However, what is the reasoning behind ...
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1answer
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Consistency of time-dependent and time-independent perturbation theory

I am confused as to how time-independent and time-dependent perturbation theories in QM give consistent results at the instant the perturbation is switched on. Suppose I have a two-level system which ...
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Infinite square well: what's the intuition behind there being no chance to measure energy in states where n is even?

In an infinite square well of width $a$ (running from 0 to $a$), the wavefunction is, $$|\psi_n\rangle=\psi_n(x)=\sqrt{\frac{2}{a}}\sin\left(\frac{n\pi}{a}x\right)$$ What's the intuition behind there ...
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66 views

$\hbar \approx 0$ and the spread of QM wave function

Is there a direct mathematical method to show that if a quantum wave funtion is initially sharply localized, then it will stay sharply localized if $\hbar \approx 0$? In that case the Ehrenfest ...
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Prove a version of the uncertainty principle

Hello this question is about the wave nature of the electron and the uncertainty principle. The question goes as follows: A finite wave train has a constant velocity $v$ and its profile as a ...
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3answers
51 views

Does the electro-dynamical lagrangian contain a (Dirac) wave-function?

Consider a lagrangian for quantum electro-dynamics. It contains the two fields: the vector $A$-potential inside $F_{\mu\nu}$ and the matter field $\psi$ (Dirac's spinor). A series of questions arise ...
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Question about Eq. 10.9 in Ashcorft and Mermin

I have a doubt concerning the assumptions made in deriving Eq. 10.9 in Ashcroft and Mermin's Solid State Physics text. We have two entities in the equation: $\psi_m (\textbf{r})$ and $\psi(\textbf{r})$...
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1answer
51 views

How to correctly apply the $L^2$-operator to a wave function?

If I have a wave function that says $$\psi = \alpha Y_1^1 + \beta Y_1^0 + \gamma Y_1^{-1},$$ then it is clearly that this wave function is an eigenfunction of $\hat{L}^2$ with its $l$-value being $1$. ...
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1answer
48 views

Can quantum black hole be in superposition state?

Quantum black hole can have electric charge and angular momentum or spin, I am wondering if a quantum black hole can be described as a probability wavefunction or not? If so can it quantum tunnels too?...