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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422 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). ...
2
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2answers
243 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 ...
2
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3answers
875 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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vote
0answers
80 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
91 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
63 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 ...
5
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5answers
8k views

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
481 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
153 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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2answers
70 views

Electrons are 3 dimensional quantized waves (wave functions)?

I thought that electron wave functions were only mathematical of were to find the electron. ...
2
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2answers
265 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 ...
0
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2answers
105 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 ...
6
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3answers
1k views

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 ...
0
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2answers
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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3answers
93 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 ...
3
votes
3answers
214 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 ...
2
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1answer
40 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 ...
0
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1answer
93 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 ...
0
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1answer
86 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
53 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
44 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?
6
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2answers
416 views

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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0answers
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 ...
2
votes
1answer
211 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 ...
0
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1answer
98 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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2answers
81 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
182 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
votes
1answer
54 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 ...
5
votes
1answer
254 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 ...
2
votes
1answer
147 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 ...
4
votes
1answer
53 views

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
137 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 ...
7
votes
1answer
370 views

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
284 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 ...
0
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0answers
70 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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0answers
25 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 ...
4
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1answer
107 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 ...
5
votes
3answers
501 views

Physical meaning of quantum operators

Let's say we have a wavefunction $\psi$ and a measurement operator $\hat A$. I understand how eigenvalues and eigenvectors of $\hat A$ describe the possible outcomes of the measurement. I also ...
3
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2answers
256 views

Wavefunctions in different Hilbert spaces

The state of a quantum system is represented by a wavefunction usually in some specific Hilbert space, .e.g of position, spin, momentum etc. But before deciding in which of these bases to decompose ...
2
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0answers
293 views

Analytic form of the normalization constant for Laughlin wavefunction

Is there any analytic form of the normalization constant for Laughlin wavefunction $$\prod_{i < j} (z_i-z_j)^{1/\nu} e^{-\sum_i |z_i|^2/4}$$ where $\nu$ is the filling factor?
0
votes
0answers
94 views

How do you determine the symmetry of spatial wave functions?

I have been reading about the ways to determine the ground of state of an atom. There are three Hund's rules in determining which electronic state is a ground state. And the second rule says you need ...
0
votes
2answers
159 views

Rectangular potential barrier

Take the usual rectangular potential barrier, that is: $$V(x)=0 \: \text{if} \: x<0 \: \text{or}\: \: x>a$$ $$V(x)=V_0 \: \text{if} \: 0\leq x \leq a.$$ I've looked at several notes and books ...
0
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1answer
149 views

How can the wave function contain all information of a system?

During my quantum mechanics lectures and in literature I sometimes hear that "the wave function, $\Psi$, contains all information of the system". This has made me feel rather puzzled so I hope you ...
1
vote
1answer
37 views

Need help on understanding mechanical wave function [closed]

My textbook states that, equation 1 : y(x=0,t) = Acos($\omega$t) = Acos(2$\pi$ft), which I understand. However the book goes deeper stating also that, t-$\frac{x}{v}$, and $\frac{x}{v}$-t I am ...
4
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2answers
652 views

State of a system in Quantum Mechanics and state vectors

I'm taking a course in Quantum Mechanics and there is something I'm not being able to fully understand. On more elementary courses on Quantum Mechanics I've been told that the idea of Quantum ...
0
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2answers
84 views

Using slope=0 technique to find most likely spherical shell

In this PDF http://riedo.gatech.edu/Teaching/Modern_Physics/hw/HW3_2010_MP_SOL.pdf problem#1, the instructor solves the question of which spherical shell (what radius $r$) has the greatest ...
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0answers
52 views

Definition of linear response kernel in terms of wavefunctions (Parr/Yang)

I'm trying to understand the derivation of the linear response kernel in Parr/Yang's "Density-functional theory of atoms and molecules". First some background information: We look at a system of $N$ ...
0
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1answer
58 views

Barycenter and relative coordinates for schroedinger equation of the hydrogen atom

Heyho, i just realized i am not sure how one gets from: $\Big(-\frac{\hbar^2}{2m_e} \Delta_{r_e} - \frac{\hbar^2}{2M_P} \Delta_{r_p} +V(r) \Big)\Psi(r_e,r_p) = E \Psi(r_e,r_p)$ to: ...
12
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3answers
465 views

Bound states of the $V(x)=\pm \delta'^{(n)}(x)$ potential?

The $\delta(x)$ Dirac delta is not the only "point-supported" potential that we can integrate; in principle all their derivatives $\delta', \delta'', ...$ exist also, do they? If yes, can we look for ...
0
votes
1answer
45 views

Fourier expansion and transform - what about the phase of the waves that i am adding?

Say we have a wave on the surface of the water and we want to describe it as a sum of other waves. So we use Fourier expansion to add waves of different wavelengths. For simplicity, say we have to ...