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.

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Understanding the behavior of light/photons inside a Laser

I am trying to establish a model inside my head of how light behaves but find it hard with all the seemingly contradicting information. For example, electrons inside a Laser are raised to a higher ...
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2answers
26 views

What the wave function looks of a particle in the infinite square well looks like after collapse for measurements of position and energy

Consider a particle in a the infinite square well from x=0 to x=L. At t=to, I make a measurement of position and get x=L/2. What is the resulting wave function at t=to? My understanding, from reading, ...
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1answer
49 views

Normalisation of a wavefunction [on hold]

If the system if found in the state: $$\psi=\sqrt{\frac{1}{2\pi}}(\frac1{\sqrt3}e^{-i3\phi}+ce^{-i4\phi})$$ what value of $c$ normalizes the wavefunction? Clearly: $$\int_0^{2\pi}\psi^*\psi ...
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67 views

Schrödinger Equation [on hold]

Thank you for putting my question on hold. If you will allow me a few days, beyond this weekend, to adequately rephrase the question. I need the time to find a local physicst/math professor to aid ...
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1answer
53 views

Probability of finding particle in infinite square well, displaced walls

Initially a quantum particle moves in a one-dimensional well ($x$-axis) from $-a$ to $ a$, $ V = \infty $ outside and $ V = 0 $ inside the well. So initially, the wave-function $$ \psi_0 = ...
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55 views

How to separate k into real and imaginary parts?

In $k^2 - \frac{\omega^2}{c_o^2} + (\tau_{\alpha} i \omega)^{\alpha} k^2 = 0$, $k$ is the wavenumber, $\omega$ is angular frequency, others are constants. How can I separate the wavenumber $k$ into ...
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34 views

Importance of bound states

While solving a potential well problem we get scattering states and bound states (if exist). Number of the bound states we get depends on the potential profile. What I want to ask is, what is the ...
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1answer
75 views

Quantum Mechanics Notation

Generally we have that $$|\psi\rangle=\int_{all space} \psi(\mathbf x)|\mathbf x\rangle d^3\mathbf x$$ and therefore $\psi(\mathbf x)=\langle\mathbf x|\psi\rangle$. When discussing the mutual ...
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29 views

Normalisation of simple wave function [on hold]

I'm currently hanging on a simple normalization of following wave function: $$\psi_1(x)=N_1\exp(-\frac{(x-a)^2}{4a^2}),$$ where $N_1$ is the normalization factor to get, and $a\in \mathbb{R}$ ...
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70 views

Has anyone published the procedure to generalize ladder operators for any potential in Schrodinger's equation?

I know that the ladder operator for the quantum harmonic oscillator \begin{align} H\psi_m = \left(\dfrac{p^2}{2m}+\dfrac{1}{2}m\omega^2x^2\right)\psi_m=E_m\psi_m \end{align} is \begin{align} A = ...
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39 views

Why position and momenta are fluctuating quantities?

In a coordinate basis we have $$\langle \Psi \mid \Psi \rangle = \int \prod_{i=1}^N d^3q_i |\Psi(\textbf{q}_1,\dots,\textbf{q}_N)|^2=1$$ This means that for any quantum state $\mid \Psi ...
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28 views

s,p,d,f Orbital visualization or simulation? [closed]

So my question is pretty straight forward and in two parts Q.1 I want to simulate the orbitals and visualize them in 3D using real Schrodinger wave function. Since the equation has partial ...
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2answers
58 views

Particle in a one dimensional box conditions

Why does the wave function have to be $C^1(\mathbb{R})$ for a finite square well but not for an infinite square well? For an infinite square well with boundaries at $x=0$ and $x=L$, we have ...
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0answers
40 views

How can I create particle-in-a-box diagrams in LaTeX? [migrated]

Interested in creating particle in box diagrams at various energy levels and dimensions. Does anyone have source code to do so or suggestions of good packages to use?
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302 views

What is a 'turning point' in WKB and why does it fail at that point?

What is meant by a classical turning point in quantum mechanics and why does the WKB approximation fail at that point?
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1answer
86 views

Is de Broglie matter wave a mass or a particle hypothesis?

I'm having difficulty understanding de Broglie matter wave hypothesis. It is a mass or a particle hypothesis? According to de Broglie a particle with mass $m$ moving at a constant speed has an ...
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1answer
46 views

How to calculate the expectation value of position vector?

$$\psi (\vec{x})=Ae^{-(1/4a^2)|\vec{x}-\vec{x}_0|^2}e^{i\vec{p}_0\cdot \vec{x}/\hbar}$$ The wave function is like this, then how is the expectation value of position vector (not position) calculated? ...
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1answer
36 views

How to solve infinite square well with exponential solution (of oscillatory type)?

Given a potential well of $V = 0$ on the interval $(0,L)$ and $V = \infty$ outside the well, I am working to solve the Time Independent Schrodinger Equation $$\dfrac{d^2}{dx^2} \psi= ...
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22 views

Valence bond wavefunction of nitrogen

Could someone explain to me how one finds the valence bond wavefunction of an atom? Take nitrogen for example, I know both nitrogen molecules have a valence-electron configuration of 2s22p1x2p1y2p1z ...
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2answers
63 views

Position space wave function of an electron

In Wikipedia I find the wave function of a free particle to be $$ \Psi(\vec{r},t) = A\,e^{i(\vec{k}\vec{r}-\omega t)}$$ This is is a plane wave moving in the direction of $\vec{k}$ with speed (phase ...
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1answer
56 views

QM: Why is there a minus sign on the Energy operator when using complex conjugate?

I understand how they get the first equation. But I have no idea why there is a minus sign on the second equation: This is from a derivation for the probability density current found here: ...
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1answer
326 views

How to find the time evolution for two-component spinor? [closed]

Taking the wave function I found here as the initial condition for the Schrodinger equation. I would like to find how the wave function will depend on time, at least for small times, and calculate ...
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1answer
82 views

Is there something wrong with quantizing two times in second quantization?

Second quantization is sometimes considered to be a bad name, because a single quantization is enough. For electrons, we can either start from a many body viewpoint and introduce field operators or we ...
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60 views

Help in solving Schrödinger equation for Hydrogen

I have almost finished getting the solution to the Schrödinger equation for the hydrogen atom (got the theta and phi component equations), but am stuck on the r component equation. Can anyone help me ...
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1answer
47 views

How do I take take the partial derivatives of the general solution to the TDSE for a free particle? [closed]

Consider the general solution to the time-dependent Schrödinger equation for a free particle \begin{align*} \Psi(x,t) &=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{+\infty} \phi(k) e^{i\left(\hbar ...
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35 views

Can someone clarify what should and should not be an operator in my verification of the 1D solution to the SE for a free particle?

I just worked out the 1D free particle solution to the Schrödinger equation. My wave function was \begin{equation} \psi(x,t) = Ae^{i(px-Et)/\hbar} \end{equation} So I plugged this into both sides ...
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4answers
173 views

Derivation of Schrödinger equation - free particle

I learn quantum physics from Alonso-Finn's book (Amazon link), there's one step of Schrödinger equation for a free particle that I couldn't understand. $$ \frac{\mathrm{d^{2}\Psi } }{\mathrm{d} ...
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3answers
121 views

Justifying the notation $\langle x\ |\ \psi\rangle$ [duplicate]

I came across this expression: $$\langle x\ |\ \psi\rangle=\psi(x)$$ How can it be justified? I understand the LHS as an inner product, and the RHS just as a function of the parameter $x$.
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1answer
124 views

Eigenvalues of the radial Schrödinger equation on a finite integration interval

There are numerous ways to estimate the eigenvalues of a radial Schrödinger equation, see http://arxiv.org/abs/math-ph/0703040 as an example. Anyhow, the formulas only cover the Schrödinger equations ...
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69 views

Why is the expectation value of ground state electron momentum zero?

I have a normalized energy eigenfunction for the ground state of Hydrogen which is $$ \Psi(r) = \frac{1}{\sqrt{\pi a_0^3}}\exp\left(-\frac{r}{a_o}\right), $$ where $a_o$ is the Bohr radius, I have ...
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45 views

Why does a plane wave leave the position of the particle unspecified?

I'm covering a book on QM, and just started recently and I'm stuck at understanding something. It says that we can describe the state of motion of a particle with an infinite plane wave equation: ...
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4answers
131 views

What does “spread of momentum” actually mean?

I was reading Feynman's lecture in which Feynman invoked his own way of explaining the uncertainty principle using single-slit experiment. There I found: To get a rough idea of the spread of ...
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0answers
199 views

writing wave function of a spinor having a spin component [closed]

The effective Hamiltonian for photonic graphene is given by \begin{equation} H=\hbar\nu_{F} {\bf \sigma}\cdot\left(q+\frac{\Delta \vec S^{\prime}}{\hbar\nu_{F}}\right), \end{equation} where ...
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24 views

What are the conditions of wave function continuity when solving for Dirac Spinors as done in “Klein paradox” paper by Novoselov?

In the paper "Chiral tunneling and Klein paradox" paper by Katsnelson, Novoselov, and Geim, they use the wave function for Dirac spinors. What are the conditions for continuity of the wave function ...
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131 views

Triangular barrier in infinite potential well

Suppose I am looking to solve the wavefunction for the following 1D potential: $$U(x) = \begin{cases}V_0\frac{a-|x|}{a}&\quad\text{for}\quad|x|<a ...
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2answers
58 views

The delta function as an eigenfunction of the position operator explanation

$\delta (\textbf{r})$ can be interpreted as a wavefunction. [...] It is non-vanishing only for $\textbf{r}=0$. [...] $\delta(\textbf{r})$ is an eigenfunction of the position operator with ...
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84 views

Normalization of wave function meaning…?

I just have one question. I'm doing a problem where I'm told to normalize a wave function, which is split up into two regions, namely where $r \leq r_0$ and $r > r_0$. My question is, why am I ...
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1answer
85 views

How does one normalize this wavefunction? [closed]

Here is the question: So I could write $ N = \dfrac{1}{{\sqrt{<Ψ|Ψ>}}} $, right? Considering the parentheses in the exponential term, it looks like a good idea to switch to spherical polar ...
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2answers
74 views

Eigenstate vs collapsed wave function

An eigenstate, or determinate state, is a state where the measurement of some observable always yields the same result. This means that the standard deviation of the observable is zero. If a ...
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1answer
40 views

Probability density function of a particle for computation [closed]

I'm writing a program, part of which relies on a particle being able to change location similar to a how a real particle would behave (pardon my physics). For example, on a grid of 100x100, a ...
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2answers
117 views

Why do wave functions need to be normalized? Why aren't the normalized to begin with? [duplicate]

Before I started studying quantum mechanics, I thought I knew what normalization was. Just pulling off Google, here's a definition that matches what I've understood normalization to mean: ...
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1answer
60 views

Fermions in a well

I have two identical fermions in an infinite potential well. They are non-interacting. How should I show that the first excited state is four-fold degenerate? Is the wavefunction just the ...
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5answers
299 views

Why do we need a wave function?

Assuming our only aim is to solve double slit experiment (or other problems that can be mapped into that). Knowing that electron does some strange thing not expected of a particle, we need a function ...
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2answers
340 views

Can expectation value be imaginary?

I was solving a problem and the result of the expectation value of an operator came out to be $-\frac{\hbar}{4}$ $i$. Is this result possible? It seems counter intuitive.
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79 views

Is it possible to reconstruct the wavefunction of a molecule from a collection of spectra?

Spectra of a molecule can be calculated if the wavefunction is known. Is it possible to do the opposite?
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37 views

What's the relation between molecular orbitals and electron density?

The way molecular orbitals are drawn represent the "encapsulated" space in which the wave function has a significant amplitude. How do I obtain from this the electron density? Is there a fundamental ...
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167 views

Problems while numerically computing band structure using k.p theory

I want to use k.p theory to numerically compute the band structure of a bulk semiconductor. The band I like to include are the lowest conduction band (cb), the heavy-hole (hh), the light-hole (lh) and ...
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87 views

What is the necessity of wave packet in studying matter wave?

I am new to this realm of physics. I have literally understood the matter wave, wave function; read the trapped electron in an infinite potential-well. But what I didn't understand is the concept of ...
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5answers
250 views

Normalizing the solution to free particle Schrödinger equation

I have the one dimensional free particle Schrödinger equation $$i\hbar \frac{\partial}{\partial t} \Psi (x,t) = -\frac{\hbar^2}{2m} \frac{\partial^2}{\partial x^2} \Psi (x,t), \tag{1}$$ with ...
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2answers
117 views

Relation between Wave equation of light and photon wave function?

Suppose in our double slit experimental setup with the usual notations $d,D$, we have a beam of light of known frequency $(\nu)$ and wavelength $(\lambda)$ - so we can describe it as $$ξ_0 = ...