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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Linear vs. quadratic dispersion relation

In wave mechanics the dispersion relation between frequency $\omega$ and wave number $k$ is linear: $$\omega_n=c k_n$$ But in quantum mechanics, based on Schrödinger's equation, one can show that we ...
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4answers
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Is the wave function of a particle re-created after a measurement stops?

Yeah, I haven't quite understood, or been told, what happens to, for example an electron and it's wavefunction, when you stop to measure it? I mean, an electron has a wave function describing it's ...
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57 views

Valence bands question

I'm currently doing solid state physics and learning about semiconductors. During the course, I have seen a lot of energy/wavevector graphs, like this one (pic from Kittel): I did not have a ...
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4answers
347 views

Does $\lvert\langle p\lvert\psi\rangle\rvert^2$ have any meaning at all?

I used to think $\lvert\langle p\lvert\psi\rangle\rvert^2$ had the meaning of some likelihood of the particle's momentum being $p$ (within some tolerance interval $\Delta p$). Now I'm just confused. ...
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56 views

Does wave function of an electron itself move?

As far as I know quantum mechanics, electrons in an atom in vacuum move accordingly a wave function (a complex scalar field), but the wave function itself does not move (except that the atom may ...
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49 views

Are Neutrons and anti-Neutrons attracted to each other over distance?

Lets create a scenario where you have a total vacuum and you're shooting into this vacuum two streams, one, a Neutron stream and the other an anti-Neutron stream and because you're curious what will ...
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3answers
73 views

Particle in a box: value for wave function $u(x)$ when potential $V(x)$ is infinity

The time-independent Schrödinger equation (TISE) is: $$ -\frac{\hbar^2}{2m}\frac{d^2 u(x)}{dx^2}+V(x)u(x)=Eu(x) \hspace{15pt}$$ where $E$ is a constant. Imagine now a infinity potential well as ...
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57 views

Angular momentum for a given Wavefunction [closed]

Problem: Give a particle in the state $\Psi = e^{\frac{-(x^{2}+y^{2}+z^{2})}{a^{2}}}(\frac{x}{a} + \frac{yz}{a^{2}})$, what are the allowed values for $l_{x}$ (and later for $l_{y}, l_{z}$). Attempt: ...
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1answer
40 views

What is the main difference between a free particle on a line and a free particle on a circle?

The energy spectrum for a free particle in a circle with radius $r$ is $$E_n=\frac{n^2\hbar^2}{2mr^2}.$$ The energy spectrum for a free particle on an infinite line is similar. If so, what is the ...
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1answer
100 views

Why are eigenspaces of a Hermitian operator mutually orthogonal? [closed]

In Quantum Mechanics, from the properties of the solution of Schrodinger's Equation inside the infinite well, is that they are: Mutually orthogonal for different eigenvalues. Orthonormal. Complete. ...
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58 views

The boundary condition for delta function

Beginning with the Schr\"odinger equation for $N$ particles in one dimension interacting via a $\delta$-function potential $$(-\sum_{1}^{N}\frac{\partial^2}{\partial ...
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386 views

How axiomatic is the symmetrization requirement (i.e. the Pauli principle)? (in QM)

I've so far always been told, that the symmetrization requirement is an axiom on the level of the Schrödinger equation and the statistical interpretation of the wave function (or it's absolute value). ...
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2answers
221 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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3answers
689 views

Who is doing the normalization of wave function in the time evolution of wave function?

In the Schrodinger equation, at any given time $t$ we should jointly add another sub equation, like $$||\psi_t(x)|| = 1$$ where $\psi_t(x) = \Psi(x,t)$, and then try to solve the two equations ...
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0answers
54 views

Width of a Gaussian wave function [closed]

Consider the wave function with probably density given in position space as follows: $$P(x,t)=|\Psi(x,t)|^2=\frac{\pi^{-1/2}\Delta p_x/\hbar}{[1+(\Delta ...
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1answer
73 views

Particle in a double delta potential, scatter states

I was studying the scatter states of a particle in a double delta potential given in this link: Double delta function well – scattering states But I dont understand how equations (20) and (21) were ...
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1answer
50 views

Quantum States, Hilbert Space and Time

I'm having troubles with the assertion "(normalizable) wave-functions constitutes (projective) Hilbert space". The standard argument I find for this seems to go as following: say $\Psi(\vec{x},t)$ is ...
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5answers
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Confused over complex representation of the wave

My quantum mechanics textbook says that the following is a representation of a wave traveling in the +$x$ direction:$$\Psi(x,t)=Ae^{i\left(kx-\omega t\right)}\tag1$$ I'm having trouble visualizing ...
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2answers
239 views

Importance of Schrodinger equation [closed]

Louis de Broglie suggested that for microparticles like electrons, wave-like properties can be applied in order to explain some phenomena. Schrodinger wrote down an equation, a wave equation, ...
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2answers
138 views

Wave packets and half-width at half-maximum

Suppose we have a Gaussian wave function and amplitude distribution function $$\psi(x) = (\frac{2}{\pi a^{2}})^{1/4}e^{-x^{2}/a^{2}}e^{ik_{0}x}, \qquad \phi(k) = (\frac{a^{2}}{2\pi})^{1/4}e^{-a^{2} ...
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61 views

Electrons are 3 dimensional quantized waves (wave functions)?

I thought that electron wave functions were only mathematical of were to find the electron. ...
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222 views

Quick question on sketching wavefunction in well

Usually for an infinite well, the sketch for n=3 level is this: Now I think if one side of the potential barrier is higher, the particle will be more likely to spend time on the left side than ...
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81 views

Relationship between nodes in wavefunction and orthogonality

I read that if I want to construct a wavefunction orthogonal to given $n$ orthogonal wavefunctions, then the new wavefunction should have $n$ nodes. Is this valid under all conditions? Is there a ...
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3answers
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Does quantum mechanics allow faster than light (FTL) travel?

Let's suppose I initially have a particle with a nice and narrow wave function[1] (I will leave these unnormed): $$e^{-\frac{x^2}{a}}$$ where $a$ is some small number (to make it narrow). Let's also ...
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53 views

In what cases and with what method does one find a time dependent probability density for a quantum system in an infinite square well?

How can one find the time dependent probability density function of a quantum system given $\Psi(x,t=0)$? Say, $\psi(x) \sim x^4$ for $0 < x < L$. How can one find the time dependant probability ...
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90 views

Finite square wall with $E > V_0$

I'm working through a problem for homework and feel as if there is a typo or I am confused. The problem is with a one sided finite square wall such as this: So the energy is more than $V_0$. I'm ...
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3answers
198 views

What is the connection between gravitons and geometry?

I know there are two ways to do quantum gravity. One can pick a background space-time (usually Minkowski flat space-time) and then at any time slice one can define the state of the universe as the ...
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1answer
34 views

What is the equation of motion for multiple simultaneous pressure waves in a medium? (In the context of stimulated Brillouin scattering)

My overall motivation is to derive the behavior of Brillouin scattering in a birefringent fiber. Brillouin scattering is a nonlinear interaction between light and sound. In classic Brillouin ...
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93 views

What are the functions of these coefficients $c_1,c_2,c_3,c_4$ in $ \psi_{sp^3}= c_1\psi_{2s}+ c_2\psi_{2p_{x}} + c_3\psi_{2p_y}+ c_4\psi_{2p_{z}}$?

Hybridised orbitals are linear combinations of atomic orbitals of same or nearly-same energies. Atomic orbitals interfere constructively or destructively to give rise to a new orbital which is what we ...
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1answer
91 views

Is it okay to put singularities into the wave function to test behavior around unstable potentials? [closed]

$$ \psi(r)=\sqrt[4]{\frac{ a}{8\pi^3 }}\frac{ \exp (-a r)}{r^{1.25}} $$ The wave function above is an example of a function that is normalizable in 3D space and $r=\sqrt{x^2+y^2+z^2}$. $$ -\psi ...
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76 views

Wave packet and group velocity?

While finding the wave function of a free particle say $\psi(x)$, my textbook says that this is nonphysical because the wave velocity is not same as particle velocity of the free-particle. I don't ...
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2answers
48 views

Quantum harmonic oscillator - Where am I going wrong?

Find the relationship between $a_+\psi_n$ and $\psi_{n+1}$ My attempt: I was able to prove that $\int{(a_+\psi)^*(a_+\psi)dx} = \int{\psi^*({a_-a_+\psi})dx}\qquad\qquad (1)$ And, ...
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0answers
41 views

Where do we get an initial wavefunction for a particle or a system?

In many QM text books, a numerical problem starts with the statement that "a particle has an initial wave function of ..." My question is how do we find the initial wave function in the first place?
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Why must $\Psi (x,t)$ go to zero faster than $\frac{1}{\sqrt{|x|}}$?

Why must $\Psi (x,t)$ go to zero faster than $\frac{1}{\sqrt{|x|}}$ as $|x|$ goes to $\infty$? According to Griffiths' Introduction to Quantum Mechanics, it must. I don't understand why, and this is ...
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35 views

How is charge separation in a polarized vacuum possible?

How is Charge Separation in a Polarized Vacuum possible? The Uehling potential provides the first correction term to the classical coulomb potential from QFT vacuum polarization: $$ V(r) \approx ...
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1answer
197 views

What is the difference between a one-particle state in the fock space and single particle wave function (in momentum representation)?

If I consider one single Dirac electron in momentum representation, I use the wavefunction $u(p)e^{-ipx}$, however if I consider an one-particle state in the Fock space I use $|p\rangle$. Should it ...
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1answer
90 views

Normalizing a wave function [closed]

A particle with mass $m$ is moving in one dimension. The wave function of the particle is $$\Psi(x,t)=Axe^{-(\sqrt{km}/2\hbar)x^2}e^{-i\sqrt{k/m}(3/2)t}$$ for $-\infty<x<\infty$, ...
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80 views

Uncertainity principle and double slit experiment?

My Understanding of uncertainty principle goes that if some particles are in same state, then their measurement of certain property (say $x$ and $p$) will be different for different particles. ...
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1answer
112 views

QM and relative phases

I recently started formally learning about QM. I have studied thus far that any global phase difference is irrelevant when taking energy expectation values. However, that is not evidently the case for ...
2
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1answer
52 views

Derive probability current density - factors of 2 discrepancy [closed]

To derive the probability current density for a particle in an electromagnetic field, we calculate $\dfrac{\partial \rho}{\partial t} = \dfrac{\partial}{\partial t} (\Psi^* \Psi) = \dfrac{\partial ...
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1answer
220 views

Which position and momentum distributions arise from some wave function?

Consider a particle in one dimension with wave function $\psi(x)$. The probability density function describing how likely it is to find it in a given position is given by ...
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2answers
130 views

Where are the worlds in many-worlds interpretation?

What does it mean in MWI for other universes to exist? Are they in some sector of spacetime beyond our cosmic horizon or is it more complicated? I'm not asking this on Philosophy SE because people ...
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1answer
121 views

Normalization of potential barrier solution

I don't understand a point in the solution attached to this barrier potential problem. Below equation 4.209, they say Assume first that the wave function on the right side of the barrier in the ...
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1answer
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Probability in Measuring Noncommuting Observables

If I have a particle in a state $\Psi(x) = e^{-x^2}$ could I calculate probability of simultaneously measuring, say, $x > 0, p_x < 0$? I understand that $p_x$ and $x$ don't commute and ...
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1answer
135 views

Wavefunction interpretations in QM

From two-slit electron-interference experiment we can infer that there is a wave $\psi(x,t)$ that can be associated with electron. The amplitude at some point is the sum of amplitudes reaching that ...
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What is the wavefunction of the Young Double Slit experiment?

I have never seen the wavefunction for this experiment and would like to know how to derive it using the Schrodinger equation. I specifically want to see how the electron wave function leaves the ...
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2answers
191 views

Why are electron wavefunctions standing waves?

How can I convince myself that wavefunctions of electrons on molecular orbitals are indeed standing waves? Is it a consequence of the fact that electrons don't drift away from the molecule? In other ...
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66 views

Wave function: what does “1% chance of finding the particle in this area” mean

Say I have 1 electron in some quantum state Defined by some wave function, and it's doing its thing fluctuating the probabilities of where it might be. What if I put a measuring device in an area ...
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24 views

Dirac equation in the presence of a defect

The 1D Dirac equation in the presence of a defect is described by a position dependent mass term known as a "kink" or "soliton". It is sign changing and tends to a constant at positive and negative ...
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1answer
103 views

In interpretations of QM where the wave function is real, what does that mean?

In a lot of interpretations of Quantum Mechanics they believe that the wave function is "real". But what does that mean? Are they saying that the wave function of an elementary particle ...