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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130 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 ...
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1answer
34 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 ...
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444 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 ...
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2answers
71 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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46 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 $N$ ...
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56 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: ...
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435 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 ...
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41 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 ...
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2answers
534 views

Schroedinger equation for hydrogen atom

I have got a problem understanding the meaning of the Laplace operator in the Schrödinger equation for the hydrogen atom. $$\Big(-\frac{\hbar^2}{2m_e} \Delta_{r_e} - \frac{\hbar^2}{2M_P} \Delta_{r_p} ...
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1answer
384 views

What does a light wave look like (3d model)

What does a light wave look like? The only models I can seem to find online are 2D waves, they just look like sin() graphs. I have seen the models of the two components of "light waves" (electric ...
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4answers
7k views

Differences between wavefunction, probability and probability density?

I am trying to understand the differences between wavefunction, probability and probability density. There are different definitions on the internet. For example: ...
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4answers
268 views

Physical intuition behind negative values for wave function?

So a positive and a positive wave function create a bonding orbital where the probability of finding an electron is summed while a positive and a negative create an anti-bonding orbital with a lower ...
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1answer
1k views

Must the derivative of the wave function at infinity be zero?

I came across a problem in Griffiths where the derivative of the wave function (with respect to position in one dimension) evaluated at $\pm\infty$ is zero. Why is this? Is it true for any function ...
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1answer
118 views

Is the photon's wave function the same as an electromagnetic wave(light)? [duplicate]

The first that i have been taught in Quantum Mechanics is the photoelectric phenomenon. Without analyzing it, it concludes that when we shine light at the circuit(roughly speaking), the work required ...
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83 views

Do quantum wave functions curve spacetime before they are measured

Do wave functions cause spacetime curvature before they are measured, or would curvature only happen upon measurement? I guess the question becomes, do quantum wavefunctions carry energy while they ...
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1answer
113 views

Width of a 1 dimensional box with same ground state energy as hydrogen atom [closed]

I am trying to find the width $L$ of a one-dimensional box for which the ground state energy of an electron in the box equals the absolute value of the ground state of a hydrogen atom. No ...
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2answers
237 views

Why is $ \psi = A \cos(kx) $ not an acceptable wave function for a particle in a box?

Why is $ \psi = A \cos(kx) $ not an acceptable wave function for a particle in a box with rigid walls at $x=0$ and $x=L$ where $$ k = \frac {(2mE)^{1/2}} {\hbar} \, ?$$ I had plugged the wave ...
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86 views

How can a solution of the time-independent Schrödinger equation evolve in space?

I understand that if the Hamiltonian does not depend on the time, the Schrödinger Equation becomes separable, so you get $$ H \psi(x) = E \psi(x) $$ and $$ \Psi(x,t) = ...
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48 views

Potential energy function for high energy continuum?

For the hydrogen atom the quantised energy levels are: $$E_n = \frac{- 13.6 eV}{n^2}\quad\text{with}\quad n = 1,2,3...$$ One peculiar property of this quantisation is that for large $n$ the energy ...
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969 views

Normalization of Momentum Eigenfunctions: the number of particles

After finding the eigenfunctions $u_p(x)=Ce^{ipx/\hbar}$ of the momentum operator just like in this UCSD lecture notes, one seeks to normalize them, so one first tries: ...
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359 views

Confusion about 1-forms as introduced in “Gravitation” (Kip S. Thorne,…)

In the book Gravitation in chapter 2, paragraph 5, they introduce the concept of 1-forms by thinking about the momentum 4-vector differently. They first introduce the de Broglie 1-form as follows (I ...
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156 views

How to predict bound states in a 1 D triangular well?

Assume we have a (single) particle in a potential well of the following shape: For $x \leq 0$, $V = \infty$ (Region I) For $x \geq L$, $V = 0$ (Region III) For the interval $x > 0$ to $x < ...
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1answer
122 views

Schrodinger's equation with negative sign

In time dependent Schrodinger's equation as given in Schrodinger's lecture (Four Lectures on Wave mechanics, Blackie & Son, 1949, pg22) he arrives at $$\nabla^2\psi-\frac{4 \pi m ...
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What is probability current in quantum mechanics?

What is probability current in quantum mechanics? Why define such a thing? I mean the meaning of probability current. I know the formula for it but I just don't get the idea of a flow of probability ...
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59 views

Normalizing a wave function in a mixed well

So I got this potential and want to solve for the even wavefunctions http://imgur.com/GKAy4nD Since it's symmetric around the origin I need only to look at the interval [0,b] and solve for the ...
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323 views

What do “ℜe” and “A*” mean?

What do "$\mathfrak{Re}$" and "A*" mean in the following equation (taken from James Binney and David Skinner's QM lecture notes, equation 1.12), \begin{align} p(S\text{ or ...
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1answer
52 views

Why do the two amplitudes need to match together through the region between the boxes?

This is an excerpt from Feynman's lectures 3; Suppose we think of the situation in Fig. 7–3, which has two boxes held at the constant potentials $ϕ_1$ and $ϕ_2$ and a region in between where ...
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1answer
814 views

Why does the wave function have to be continuous? [duplicate]

When solving one dimensional problems in quantum mechanics it is often assumed that the first derivative of the wave function is continuous. What justifies this assumption?
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109 views

Why can the probability function for a particle in an infinite square well be larger than 1?

For a particle in a one dimensional infinite potential well of width $L$ the probability function is: $$P_n(x)=\left(\frac{2}{L}\right)\sin^2\left(\frac{n\pi x}{L}\right)$$ for $0\leq x\leq L$. The ...
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3answers
619 views

Electron as a standing wave and its stability

1. When it was an era of classical mechanics we used to believe in the Bohr's atomic model. It interpreted electrons as particles (although I couldn't understand how come Bohr who interpreted ...
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522 views

Double slit experiment observation

In the double-slit experiment, if you shoot particles through the slits one by one and observe which slit they travel through, is there still an interference pattern on the screen behind the slits? If ...
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172 views

Wave Function concept

What do we mean when we say wave function of electron? Does it mean wave nature of electrons? I am really confused.Without clearing this confusion i cannot proceed to molecular orbital theory.I am ...
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4answers
176 views

Isn't the 'slit' in a double-slit experiment also a wave?

I'm new to QM so excuse my naivety. I was watching an online MIT QM course that described the double-slit experiment (with electrons) when it occurred to me that I have a question. In the video, the ...
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2answers
84 views

Where does the factor of $x$ come from in this formula for expectation value?

Given the normalised ground-state wave-function: $$\Psi(x, t)=\begin{cases} \sqrt\frac{2}{d}\cos(\frac{\pi x}{d})e^\frac{-i\hbar\pi^2t}{2md^2} & \ \lvert x\rvert<\frac{d}{2}, \\ 0 & ...
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24 views

Cancelling waves and preservation of energy

In quantum physics, a particle is "defined" by a wavefunction. If you would take 2 particles with the same wavefunction, and negate one of them. They would cancel each other other out. Take for ...
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28 views

Solutions to time-independent Schrödinger's equation with symmetrical (even) potential [duplicate]

A problem from Griffith's Introduction to Quantum Mechanics asks to prove the following: Given a symmetric potential $V(x)$ $(=V(-x))$, the solutions to the time-independent Schrödinger's equation ...
6
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2answers
178 views

What state the wave function collapses into after an inaccurate measurement?

I'm watching MIT online lectures Quantum Physics I (roughly from one hour mark in the video). The lecturer explains wave functions that describe "Stationary States" that consist of a single energy ...
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1answer
115 views

The definition of the vacuum state of quantum field by path-integral

In the review Entanglement entropy of black holes by Sergey Solodukhin (arXiv:1104.3712, equation 13), I see a definition of vacuum state of quantum field by path integral over half of the total ...
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1answer
38 views

$\sqrt{\frac{\omega ^2}{c^2}-k_z^2}$ in cylindrical harmonics

The radial component of the solution of the wave equation in cylindrical coordinates is $$J_\nu \bigg(\rho\sqrt{\frac{\omega ^2}{c^2}-k_z^2}\,\,\bigg).$$ But I always thought that $\frac \omega c$ ...
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0answers
51 views

Transfer function of a space varying wave equation

$$\frac{\partial ^2 \psi}{\partial x^2}-\mu \epsilon \frac{\partial ^2 \psi}{\partial t^2}-\mu \sigma \frac{\partial \psi}{\partial t}=0$$ Is the wave electromagnetic wave equation in lossy, source ...
3
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1answer
138 views

Plane wave expansion of cylindrical functions:Summation of the Hankel functions

I understand that; in cylindrical coordinates, the basic solutions of the Helmholtz equation are of the form Hankel function of integer order times a complex exponential term ...
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3answers
284 views

Constructing solutions to the time-dependent Schrödinger's equation

The following question is from David Griffiths' Introduction to Quantum Mechanics: Problem 2.13 A particle in the harmonic oscillator potential starts out in the state $$\Psi(x,0) = A[3 ...
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5answers
161 views

Does measurement change the evolution of wave function?

Basically any measurement is on wave function $|\psi\rangle$ is done by operator $X$ such that $X|\psi\rangle$ results observable $x$ with some probability. But what happens to $|\psi\rangle$? Does ...
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72 views

Does a free electron, one that's not either in an atom or a wire, have an associated wave-function?

Would a free electron, one that's not either in an atom or moving through a wire, but moving through empty space on its own, have an associated wave-function? Or, is an electron described as a ...
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1answer
86 views

Solution of the Radial Part of the Schroedinger Equation [closed]

The general Schroedinger Equation is: $$\left[-\frac{\hbar^2}{2m}\triangle +V(r,\vartheta,\varphi)\right]\psi_{nlm}=E\psi_{nlm}$$ When considering free waves, i.e. $V(r,\vartheta,\varphi)=0$ and a ...
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1answer
168 views

How to visualize a Schrödinger cat state?

I recently read about Schrödinger cat states (SCS), which are basically a superposition of two coherent states $|\alpha\rangle$ with opposite phases, that is, $$ |cat\rangle = |\alpha\rangle \pm ...
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1answer
60 views

Property of the wave functions of a free particle

How can I show that the following holds? $$\langle nlm\mid \partial_z^2\mid nlm\rangle=-\int_0^{4\pi}d\Omega\int_0^{\infty}drr^2\left|\partial_z\psi_{nlm}\right|^2$$ The wave functions of a free ...
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2answers
110 views

How do phase carries structural information about the function? [closed]

Suppose you are on a railway platform and you hear the sound of train coming towards you. Now, Using Fourier transformation we can convert the time domain function (here take sound as a function) ...
3
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140 views

Time evolution of a wavepacket

I do not understand why if $H\psi = E\psi$, then the time-evolution of the wavefunction is given by $e^{-iEt/h}\psi(x)$.
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57 views

For an event that can occur in many ways, why is the wavefunction of the event the sum of wavevfunction for each way separately?

The wavefunction of identical particles is given as: $$\psi_{1,2} (x_1,x_2) = \psi_1(x_1)\psi_2(x_2) + \psi_2(x_1)\psi_1(x_2)$$ . Why is it so? Why is it the sum of the two states? What is the ...