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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Wave packets not satisfying the Schrödinger equation?

The time-independent Schrödinger equation of a free particle in 1 dimension is $$ \begin{equation} -\frac{\hbar^2}{2m}\partial^2_x\psi(x) = E\psi(x) \end{equation} $$ which has solutions in form of $...
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Proof that the momentum operator is hermitian without assuming the wavefunction approaches zero at infinity?

I am currently taking my second semester of quantum mechanics. For a number of proofs in the course, we have used the assumption that the wavefunction goes to zero at infinity. We have simply used the ...
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Why are numerical solutions for the Schrödinger equation necessary?

Suppose a particle in free space given by: $\psi(x,t) = Ae^{ik(x-\frac{\hbar k}{2m}t)} + Be^{-ik(x-\frac{\hbar k}{2m}t)}$ Why are numerical solutions necessary in order to plot this? Why can't ...
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How does the wavefunction of an electron “decollapse”?

In quantum theory, when an electron is sent through a slit (or multiple slits),the electron is described using probability amplitudes and is said to be in a superposition of multiple quantum states. ...
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identifying number of node of an arbitrary wave function

Given an arbitrary wave function, what is the most general way to identify number of its nodes? By arbitrary, I mean we don't have any predefined conditions (like wave function of an atom, a harmonic ...
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Standing Wave in a transmission line and Resonance

let's consider a transmission line of length L closed on a mismatched load. So, there will be a travelling wave and a reverse travelling wave: V(z) = V+(z) + V-(z) My question is: will there always ...
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What happened to the factor of $\pi$ in this question?

$\\ $ I was going through the answer to this problem, when I noticed that a factor of $\pi$ in the denominator disappeared and a factor of 4 appeared in the numerator when the author started ...
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134 views

Are Imaginary Numbers Really “Imaginary?” [duplicate]

I find the naming convention of “Imaginary” misleading, as it does give a sense that the quantity is merely an abstract construct used to mitigate the difficulties of performing some mathematical ...
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Understanding quantum models

In quantum mechanics we have different models like the infinite and finite square well, potential barrier, etc. What I don't understand is how these are applicable to real life situations. For example,...
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Why doesn't the nucleus have “nucleus-probability cloud”?

While deriving the wave function why don't we take into the account of the probability density of the nucleus? My intuition says that the nucleus is also composed of subatomic particles so it will ...
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What is The Heisenberg Uncertainty Principle Making Statements About?

Non-physicist here, trying to understand details about Heisenberg's uncertainty principle: Watching the The more general uncertainty principle, beyond quantum about the uncertainty principle I came ...
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Constructing many-body densities from Kohn-Sham orbitals

In many electronic structure methods, one solves "effective" one-particle Schrödinger equations for one-particle wavefunctions. In my case, I have Kohn-Sham orbitals from a DFT calculation. The ...
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Property of the time evolution operator preserving the norm of the wavefunction

Since the time evolution unitary operator preserves norm, if applied to any system say electron whizzing around its orbitals, no matter what time we consider would it always have the same probability ...
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Using FFT to find time-dependence of quantum mechanical free particle?

I am trying to visualize the time dependence of a free particle given an initial wave-function using Python and I just wanted to know if I could use the in built FFT implementation from NumPy to find ...
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The particle in a box problem

I'm studying undergrad level chemistry with no strong background in physics. So the problem is a little confusing to me. A few questions for clarification: Using the electron on a 2-dimensional box ...
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48 views

Wavefunction of an electron after a slit

To properly understand the double slit experiment with electrons, you need to know what is the wavefunction of the electron after it passes through a slit. This wavefunction cannot be a plane wave. ...
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Can the functions for states with definite momentum be used as basis for the space of all realistic wave functions?

I am really confused about this. I know that functions of definite momentum and position can be used as basis and all wave functions can be written in terms of these basis functions. But do the basis ...
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What is the Fourier Transform of the spatial portion of $Ψ(x,t)=A\exp(-b|x-2|)\exp(-i\omega t)$

What is the Fourier Transform of the spatial portion of $\Psi(x,t)=A\exp(-b|x-2|)\exp(-i\omega t)$? I'm not sure how to do it for the "spatial portion". I've only done Fourier transforms for ...
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Black hole wave function

Does a black hole have a wave function? Matter falling into a black hole has a wave function. Is the wave function of this matter destroyed or converted to information on the surface of the black hole?...
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50 views

Why does a phase shift not alter the physical characteristic of the free particle wavefunction? [closed]

I am attempting to solve a homework problem from the MIT OCW 8.04 Quantum Physics I Course. Here is a link to the problem (it is problem 5): I will rewrite the problem statement here. We wish to ...
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Quantum waves as waves of space itself?

Are there any interpretations of quantum mechanics were quantum waves are waves of space itself? I'm not talking about gravitational waves, more like pilot-wave theory. There seems to me like it would ...
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60 views

Why does the choice of origin affect the wave function?

Consider a particle in a 1D-Box. The box ranges from x=0 to x=l in the first case, and from x=-l/2 to x=l/2 in the second case. The only difference I see is that the origin is shifted. On solving ...
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59 views

Differentiability of wave function at boundary in infinite square well

I was told in class that a wave function should have the following properties: Finite and single-valued Continuous Differentiable Square integrable But if we consider the wave function in an ...
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Question on modified particle in a box [on hold]

If say, I have a particle bound in an infinite well where the floor is very slightly sloping. How would I sketch a possible wave function when the energy is E1(no nodes)? How do we do this ...
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181 views

Does a non-stationary state for a single particle with a nondegenerate spectrum necessarily have fluctuations in probability density?

Suppose we have a single particle in 1D, with wavefunction $\psi(x,t)$, obeying the Schrödinger equation in position space: $$i\hbar\frac{d\psi(x,t)}{dt}=\left(-\frac{\hbar^2}{2m}\frac{\partial^2}{\...
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52 views

Is it possible to construct a state for harmonic oscillator given the mean energy?

The harmonic oscillator is defined by the mean value energy $\langle E\rangle=\frac{2}{3} \hbar\omega$. Can we have a wavefunction which describes such a state? Any help is appreciated. Is it ...
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Is there an accepted way to plot a wave function and the potential?

When using the time-independent Schrodinger equation and finding a wave function $\psi(x)$ for a given potential $V(x)$ is there a consistent way to plot these two objects on the same image that takes ...
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Writing operators in the position basis

To calculate an expecation value in quantum mechanics of some operator $\hat A$ you can generally write it in Dirac notation $$\langle \hat A\rangle=\langle\psi|\hat A|\psi\rangle.$$ In the position ...
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Does Hatfield give the correct 1st excited state for a scalar field's wave-functional?

Hatfield's QFT textbook gives a scalar field $\phi(\vec{x})$'s first excited state as $$ \Psi_1[\tilde\phi] = \left(\frac{2 \omega_{k_1}}{(2\pi)^3}\right)^{\frac 1 2} \tilde\phi(\vec{k}_1)\Psi_0[\...
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Are wave functions built of other wave functions?

I have heard the term wave function used in a number of contexts describing both quantum objects (electrons, etc) and more macroscopic objects (atoms, birds, cats, etc). Is it correct to say a lithium ...
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75 views

What is evolving with time?

In Griffiths, we are told that the expansion coefficients of the stationary states are simply complex numbers: $$\Psi(x, \ t) \ = \ \displaystyle\sum_{n} c_n e^{-iEt/\hbar} \psi_n(x)$$ How do we ...
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How is the wave function viewed as the quantum state?

I am not sure how the wave function can be viewed as quantum state. I begin with the eigen-equation $$A|\psi\rangle = a|\psi\rangle$$ If $A$ is a $n$ dimensional matrix with different eigenvalues $...
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Double well potential and choosing coefficients

During lecture on single potential well, my professor had the following wavefunctions for the three regions: $\psi(x) = e^{\kappa x}\ for \ x<-L$ $\psi(x) = B\cos(ikx)$ for $-L<x<L$ $\...
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How does quantum computing work if the wavefunction has no reality?

This is probably a dumb layman question but as I understand it quantum computing makes use of the superposition principle in which a qbit can be in more states at once until it’s observed. A ...
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In quantum mechanics, which concept caters for light rays?

If photon wavefunctions are omnidirectional and don't have a definite size, how comes those from the Sun don't all collapse on Mercury and some do actually reach Earth ? I understand that ...
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59 views

Energy or a piecewise defined wave function in an Infinite Square well

So I'm asked to determine the most probable measured energy value of a particle in an infinite square well with wave function $$\psi(x)=\begin{cases} Ax, & 0< x<\frac{a}{4} \\[1em] ...
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101 views

What made Born interpret $|\psi|^2$ as a probability density?

What was Born reasoning when he introduced the rule that $|\psi|^2$ could be interpreted as a probability density?
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Does the second derivative of wave function have to be continuous? [duplicate]

I am very new to quantum mechanics and I have a question about wave function in time-independent schrodinger equation. In Beiser modern physic, they say the first derivative of wave function should be ...
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177 views

Question on some basic principles of quantum theory [closed]

I asked a physicist (former head of the physics department in a university) about some of the basics of quantum theory and the double slit experiment. Here is his reply. Are any of these points ...
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What is a rigid wave function?

The London equations prior to BCS that describe superconductivity require assuming the wavefunction describing the superconducting pair of electrons to be rigid. I've been looking all over trying to ...
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Does the wave function of a particle collapse if info about an observable is available in seperate chunks for many observers?

To start, I just started learning QM today so... keep that in mind. What I was trying to say is: suppose (for example) there is a box with a subatomic particle in it, the box is a 3D space so we plot ...
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Rationalizing the current operator

In eq. 1.191 of Mahan Many-Particle Physics, the current operator is defined as $$j(r)=\frac{1}{2}\sum_ie_i[v_i\delta(r-r_i)+\delta(r-r_i)v_i].$$ I'm trying to make some sense of this definition. I ...
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Probability in quantum physics of a wave function

I have this time-dependent wave function from solving a 3-component Schrodinger's equation, $$\psi(t)=-\frac{2}{9}(-2, 1, 2)^T+\frac{2}{9}e^{3i\omega t}(2,2,1)^T+\frac{1}{9}e^{-3i\omega t}(1, -2, 2)^T$...
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Can a Hermitian operator $A$ bring a wavefunction $|\psi \rangle$ out of Hilbert space?

I recently learned about an example where an operator $O$ (not Hermitian) acted on a wavefunction $|\psi \rangle$ and carried the wavefunction out of Hilbert space, i.e. $O|\psi \rangle$ is not in ...
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General solution of a particle in a box

The general solution of particle in a 1D infinite potential well(width L) is given by: $$\psi(x,t)=\sum_n a_{n}.\sqrt{\frac{2}{L}}.\sin\bigg(\frac{n\pi x}{L}\bigg).\exp\bigg(-\frac{ iE_n.t}{\hbar}\...
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How does $\psi(x) =\exp(\frac{iq}{\hbar}\int^xA(x')\cdot dx')\phi(x)$ remove the gauge field for a free particle?

In what sense does writing $$\psi(x) =\exp(\frac{iq}{\hbar}\int^xA(x')\cdot dx')\phi(x)$$ "formally remove the gauge field" for a free particle in the Hamiltonian $$H\psi=\frac{1}{2m}(-i\hbar\nabla -...
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Does the ground state of the Schrödinger equation, in any number of dimensions, always have constant phase?

I just read this argument in this paper (PDF). It suggests that, from variational principles, you can show that you can always lower the energy of a state by making the phase constant, thus resulting ...
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Connection between Schrödinger equations for a finite triangular well and a finite square well

Suppose we solve the Schrödinger equation, \begin{equation} -\psi''(x) + V(x) \psi(x) = -|E| \psi(x), \end{equation} where two cases are considered, $V(x) = -V_0$ (square well) and $V(x) = -V_0 (1 - |...
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General wave function equates to one after equating Euler's identity. Why?

Am typing on my phone, so apologies for any mistakes. Basically we know a general wave function taken as an example to be $\psi = e^{i(kx-\omega t)}$ where $k=2\pi/\lambda$ and $\omega=2\pi f$. Euler'...
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Odd potentials in TISE

When we have an even potential we say that it has an even and odd parity wavefunctions, cf. e.g. this & this Phys.SE posts. What about an odd potential? For example, two delta functions centered ...