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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Relativistic Velocity [closed]

As a particle has enough relativistic velocity, it’s mass should have a noticeable increase. How does this translate into the particle’s wave function? Is there a difference between an elementary ...
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Probability current calculations

I have a question about the probability current density. Because I cant really understand the meaning of that (how can we relate something real like a current to something abstract such as probability)...
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Are particles literally waves or just abstract probability waves?

In introductory quantum physics, particles are described by the Schrodinger equation wave-function, which describes only an abstract probability wave. But in quantum field theory, particles are ...
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Symmetric infinite well potential

Assume we have the following potential : $$ V\left(x\right)=\begin{cases} 0 & -\frac{L}{2}\leq x\leq\frac{L}{2}\\ \infty & else \end{cases} $$ The wave function for a particle in this well ...
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Bound states and scattering states - Time-dependent Schrödinger equation

If we have a quantum system described by the time-independent Schrödinger equation (TISE): \begin{equation} -\frac{\hbar^{2}}{2 m} \frac{d^{2} \psi}{d x^{2}}=E \psi \end{equation} We have two possible ...
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Relation between Matrix mechanics and Wave mechanics [closed]

What is the relationship between Hamiltonian operator (matrix), position operator (matrix) and momentum operator (matrix) in Matrix mechanics and wave mechanics?
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Weak solution of Schrödinger Equation

Consider a particle in a box $\Lambda = [0, L]$. The wavefunction $\psi \in L_D^2(\Lambda)$ where $D$ denotes a Dirichlet Condition $\psi(0)=0=\psi(L)$. We have, then $$ - \frac{\hbar^{2}}{2m} \frac{d^...
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Problem Regarding Quantization in Goodstein's Book

This question regards what is stated at page 65, Goodstein, States of Matter. We want to consider a free particle in one dimension, with movements restricted to a line of lenght $L$; so in practice we ...
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Is there an equivalence between the creation of a wavefunction and the collapse of a wavefunction?

I am thinking here of how creation vs. absorption compare for a photon. A single photon may be emitted when an electron in an atom returns down to the ground state from an excited state. In a ...
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Probability of two electrons of different energy levels contained in a single infinite potential well being found in same region

What is the probability of two electrons in a single infinite potential well centered at 0, one in the ground state, the other in the first excited state, being in the same region? I know by the Pauli ...
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Normalization of a wavefuntion [closed]

I am working with the following wavefuntion which describes two entangled photons. I need to normalize it over the frequency domain, $\omega_\alpha$ and $\omega_\beta$ are the frequency of the ...
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Wave function and speed of light

When a photon is generated, it travels at the speed of c in the form of propagating electromagnetic wave until the photon interacts with something else to have its energy absorbed or converted. Is ...
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Origin of probabilities in Quantum Mechanics?

The non-normalized wavefunction of a general qubit is given by: $$|\psi\rangle=A|0\rangle+B|1\rangle.$$ The complex amplitudes $A$ and $B$ can be represented by two arrows in the complex plane: Now ...
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Why must systems of identical particles be either totally antisymmetric or totally symmetric? Why can there not exist a mixture?

I am reading chapter 6 of Sakurai's Modern Quantum Mechanics and have come across the 'symmetrization postulate', which tells me that for any given system of identical particles, all states must ...
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How does the electron understand that it being observed in the double slit experiment?

I was reading about the double slit experiment that proved the wave and particle nature of electron. I read that electrons give a diffraction pattern when they are not observed (wave nature) and ...
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Problems deriving the Quantum Hamilton-Jacobi equation

This is my first question at Physics SE so please be kind. I am well versed in the etiquette over at Math SE, but not so much here. Anyway, I thought this question was better suited to this site ...
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Matrix elements of operators in position representation

In a lecture note, it is written $$ T_{ij} = \langle \phi_i| \hat{T} | \phi_j \rangle = \int d^3 \vec{r} \phi_i^*(\vec{r}) T(\vec{r}) \phi_j(\vec{r}) $$ How to obtain the second integral form from ...
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Do “functions” always refer to “wavefunctions” in quantum mechanics?

For example, what do we mean when we say that “Operator acts on the function that follows it”? What are the examples of “functions” that operators act on (in quantum mechanics)?
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Infinite linear potential well?

I am currently learning and solving Schrodinger's time independent equation for particles under various 1D-potentials. Would it be possible to have a mix of a linear potential (of the form $U(x)=Fx$ ...
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Why is the first derivative of the time-dependent Schrödinger equation continuous? Where does it come from?

I was taught in first year physics that the first derivative of the time-dependent Schrödinger equation had to be continuous. However I was never taught (or at least I don't remember) the reason why. \...
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Is there interferences between 2 electron wavefunctions?

The 2 slits experiment done with 1 electron shows interference from the "splitted" wavefunctions. EDIT: as precised in an answer, it is after many electrons goes in the experiment that the ...
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What is the physical justification for the boundary conditions of the Schrödinger equation for an infinite potential well?

All the literature says that the physically meaningful solutions to the Schrödinger equation in an infinite potential well must fulfill the boundary condition that the wave function is $0$ at the ...
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Is the complex conjugate of the amplitude of an electron wavefunction equivalent to the amplitude of the corresponding hole?

Is the complex conjugate of the amplitude of an electron wavefunction equivalent to the amplitude of the corresponding hole? Say I consider a wavefunction of an electron that has the amplitude A. If I ...
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Fourier transform of a real initial wavefunction

Consider the initial wavefunction given by: $$ \Psi (x,0) = \sin(k_0 x).$$ I've been taught that in order to time evolve a wavepacket one must first find the momentum space representation of the ...
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Are there experiments that show that the electron wave function can be point-like? [closed]

I know that there are scattering experiments that show that electrons act like structureless particles up to extremely small scales. But in these experiments the electrons are moving, so their wave ...
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Why does the wavefunction of a particle spread out after a measurement?

Quantum mechanics states that the wave packet of a particle "spreads-out" in position again after a measurement on this particle has been made. Is this spreading or "dispersion" ...
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How do I normalize the relativistic wavefunction in general?

https://en.wikipedia.org/wiki/Spacetime_algebra#Relativistic_quantum_mechanics claims that the wave-function can be written using geometric algebra as follows: $$ \psi=R(\rho e^{i\beta})^{1/2} $$ ...
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Is there a limit of wave function splitting?

It is possible to split the wave function (for example using a semi mirror like in Wheeler delayed choice experiment). I wonder what happens if we split it many times. My "though experiment" ...
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Measurement of non well-defined magnitudes (position)

Lets consider an hydrogen atom (superposed states) and the measurement of it's angular momentum ($\hat{L_{z}}$, in this case) since at least is defined. I imagine the measurement could be something ...
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Relating the Minev et al experiment to Brun QTT survey

I have been studying from many angles the groundbreaking/now renowned Minev et al experiment: To catch and reverse a quantum jump mid-flight [1]. I have many questions on this complex/intricate setup ...
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What are the necessary and sufficient conditions for a wavefunction to be physically possible?

Often times it is stated in books that a quantum state is physically realizable only if it is square integrable. For example in Griffiths (2018 edition) page 14 he stated Physically realizable states ...
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Hilbert space in Dirac's representation

I've been reading some old posts here on physics stack exchange and I realized something that have never ocurred to me before. Let $\mathscr{H}$ be a Hilbert space over $\mathbb{C}$. An orthonormal ...
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Correct interpretation of $\langle x | \psi \rangle$?

Suppose $|x\rangle$ is an eigenvector of the position operator $\hat{x}$ and let $|\psi\rangle$ be an arbitrary state on this Hilbert space. What is the correct interpretation of the complex number $\...
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What is the significance of a Hilbert space? [closed]

I see the term Hilbert space thrown around a lot. At first I thought it is just when you have complex vectors and define an inner product between them. However, it seems to be a lot more than that ...
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Time dependent wave function of a particle in a gravitational field

I found this great question about the solution of the Schrodinger equation for a particle in a constant gravitational field, but the solution they wanted is to the time independent Schrodinger ...
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$V(x)=V_0\sin^2(k_0x) $ potential, 1 dimensional [closed]

If I have a potential like this: $$V(x)=V_0\sin^2(k_0x) $$ where $k_0^2=2m/h^2E_*$ how can I prove that the wavefunctions are: $\Psi_q(x)=e^{iqx}u_q(x)$ where $qe[-k_0,k_0]$ and $u_q(x)$ is periodic ...
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Is a wave function a ket?

I just started with Dirac notation, and I am a bit clueless to say the least. I can see Schrödinger's equation is given in terms of kets. Would I be correct to assume if I were given a wavefunction, ...
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Why does the antibonding orbital has higher energy (than the bonding orbital) if the Coulomb repulsion is lesser?

Depending on its strength, the attractive double dirac delta potential shown below can support two bound states. They are called the bonding and the antibonding orbitals as shown in the figure below ...
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Set of probabilities distributions inside a infinite square well [duplicate]

Its been some years since I did the infinite square well. I am doing an econimics problems with probability distributions and I vaguly remember there being a name for either the wave functions in the ...
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What's $k$ in the wave equation (Quantum Tunneling)? [closed]

Given the wave function $\psi(x)= A_1\,e^{i\,k\,x} + A_2\,e^{-i\,k\,x}$ that describes a wave being transmitted and reflected on a potential barrier. In this context I find different notations for $k$:...
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Why use a path integral if we have a general solution to the Schrödinger equation? [closed]

In this answer, the general solution to the Schrödinger equation is given, and is also included here. In my QM class we talk a lot about this equation, but we haven't seen path integrals yet, and I ...
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Normalisation of wavefunction given by the form $Ae^{i(kx-wt)}$

Question 1. Let's say that the wavefunction is given in the form $$\Psi(x, t) = Ae^{i(kx-wt)}$$ Then because of the normalisation condition, the following should hold. $$\int \Psi^*\Psi dx = A^2 \int_{...
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Proof bound states exist on vanishing, negative potentials in 1D

I want to prove the following: Show that for any one dimensional, time independent potential $U(x)$, where $\lim\limits_{x \rightarrow \infty}{U(x)} = 0$ and $\int_{-\infty}^{\infty}U(x) < 0$ ...
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One-body operator for fermions - equality

I am reading Modern Many-Particle Physics by Lipparini. In chapter 1.5 he talks about the matrix elements of the one-body operator: $$F_1 = \sum_{i=1}^{N}f(x_i)$$ He mentions that the matrix elements ...
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Can we make a symmetric wavefunction out of two anti-symmetric wavefunctions?

And, if so, then can be say that we've made a boson out of two fermions? Mathematically, If f=fermion=f(x,y) then b=boson=[f(x,y)-f(y,x)]/2
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What happens to a function generator waveform when another capacitor is added in parallel with an existing capacitor in a circuit?

I am trying to gain an understanding of the first-order response of RC circuits and measurement of capacitance in a capacitive sensor using function generation and oscilloscopes. I had a question ...
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Proper way of adding parameters to a test wave function

So experimenting with the variational method, I thought of a test wave function for an infinite deep well system, $$\Psi(x) = N(a^2-x^2) \text{ for $-a$ < $x$ < $a$}$$ and $0$ everywhere else. ...
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Eigen-energy in Finite Quantum Well

So I'm a beginner at quantum mechanics and I'm learning about finite quantum wells. I've been stuck on an example on how to find Eigen-energies in conduction and valence bands of the quantum well ...
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Energy Levels in Double Finite Well potentials [closed]

Why is there a behaviour where $E_1$ and $E_2$ are close to each other? This question is already answered before but I did not understand the explanation about symmetric and asymmetric terms as I do ...
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Condition for a trial wavefunction to determine whether or not it will lead to bonding in an ion

Suppose we have some ion such as $H_2^+$ and we produce some trial electronic wavefunction. For example, we take the simple trial wavefunction made up of a single 1s orbital of the hydrogen atom ...

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