Wave function Definition and 878 Threads

hello, is the wave function of a photon is as same as the classical wave exhibited by a group of photons ? If no, what is the relationship between the wave function associated with a single photon and the classical wave which describes the behavior (such as diffraction) of light (a group of...

A wave function is a function in a Hilbert space of functions. When representing a physical sytem, what are the conventions for defining the domain and codomain of the wave function? For example, is the domain always the scalar variable representing time? Is the codomain a set of finite...

Wave function ψ(x,t) is a fuction of probability which depends on time example Ψ(x,t)=1/(c-v)t Let's suppose its a function of probability It depends on time and it affects space. Is this is a definition of wave function ? (I know wave function squuared gives probability...

Homework Statement Show that the operator O = i\frac{d^{3}}{dx^{3}} has real eigenvalues Homework Equations Differentiate a wave function 3 times The Attempt at a Solution I know the process of differentiating a wave function (as many times as you like) and it giving the wave function back...

Is this proven that wave functions extend to infinity, or is it just a theory? What makes them assume that it extends to infinity?

http://physicsworld.com/cws/article/news/2013/may/23/quantum-microscope-peers-into-the-hydrogen-atom http://io9.com/the-first-image-ever-of-a-hydrogen-atoms-orbital-struc-509684901 they are claimed to be images of the actual wave function of hydrogen. Does this mean that wave function is a real...

Is the wave function ( ex. electron wave function) just a mathmatical equation or a real physical object? I know that it's widely known that it's just an equation however some researchers say that they have proof that it's real. Here is the link...

So let's say I shoot an atom from A to B. If it interacts with other atoms, electrons or photon's, the wave function collapses right? And the particle exists in our 'normal' world, no quantum tunneling etc. And it looks as if it was a normal particle all along right? But let's say it goes from...

The Hamiltonian operator in the equation i×h/2π×∂/∂t×ψ=H×ψ(where 'i' is the imaginary no.,'h/2π' is just expanded form of the reduced Planck constant,'∂/∂t' is the partial derivative with respect to time 't' and ψ is the wave function) is,as I recall,H=I+V(i don't know how to get those carets...

Homework Statement So it says solve this wave equation : [y][/tt] - 4 [y][/xx] = 0 on the domain -infinity<x<infinity with initial conditions y(x,0) = e^(-x^2), yt(x,0) = x*(e^(-x^2)) Homework Equations I used the D Alembert's solution which is 1/2(f(x+ct)+f(x-ct)) + 1/2c ∫ g(z) dz The...

Hello,I am new to quantum mechanics.I just want to clear this equation: ψ(x) = ∑n anψn(x) What does this actually mean?Is this equation telling us that the system is moving as a wave? Or,as I think,for example let's suppouse we have 2 electrons in a system,and the wave function becomes this...

My wave function: ##\psi_2=N_2 (4y^2-1) e^{-y^2/2}.## Definition of some parts in the wavefunction ##y=x/a##, ##a= \left( \frac{\hbar}{mk} \right)##, ##N_2 = \sqrt{\frac{1}{8a\sqrt{\pi}}}## and x has an arrange from ##\pm 20\cdot 10^{-12}##. Here is my integral: ##<x^2> =...

Homework Statement Hi all, I've been working on this assignment for some time now and seem to be stuck before I even get going! So, The wave equation: d^2 u(x,t) / dx^2 = d^2 u(x,t) / dt^2 can be written as: du/dt = v dv/dt = dw/dx dw/dt = dv/dx w = du/dx I need to solve this...

Consider a potential well in 1 dimension defined by $$ V(x)= \begin{cases} +\infty &\text{if}& x<0 \text{ and } x>L\\ 0 &\text{if} &0\leq x\leq L \end{cases} $$ The probability to find the particle at any particular point x is zero. $$P(\{x\}) = \int_S \rho(x)\mathrm{d}x=0 ;\forall\; x \in...

why is psi = cos (k r - w t) + i sin ( k r - w t) = e^ [ i ( k r - w t)]? my question precisely is why not: 1. psi = sin (k r - w t) + i cos ( k r - w t) ? 2. psi = sin (k r - w t) + i sin ( k r - w t) ? 3. psi = cos (k r - w t) + i cos ( k r - w t) ? why not any of these three? is...

Homework Statement Find Fourier series of f(x) = Acos(\pix/L) I know how to do this, I just don't know the value of L. If it's equal to \lambda/2, then I know the solution. But the question does not specify the value of L. L is just the length of the entire wave that I'm working with, right? If...

I am curious if the constants for wave functions for a particle in a box can be both +/-...because constants I've applied for wave functions have always been +...

Hi, I want to calculate the position-wave-function of a system of two free electrons with momenta k1 and k2 (vectors). 1. Homework Statement So, I want to have Psi_(k1,k2)(x1,x2) for a state |k1,k2> I also know that <k'|k> = (2Pi)^3 Delta(k-k') The Attempt at a Solution I tried the...

Homework Statement Normalize the wave function ,\psi(x), where \psi(x)=\frac{1}{1+ix}. Homework EquationsThe Attempt at a Solution \langle\psi\mid\psi\rangle= \int_{-\infty}^{\infty}\frac{1-ix}{1+x^2}\frac{1+ix}{1+x^2}dx=\int_{-\infty}^{\infty}\frac{1}{1+x^2}=\left...

Take the famous double slit (thought) experiment. The wave function for the photon is a superposition of two orthogonal states, one for each slit passage. But it is claimed to collapse into one of these two states when the photon hits the screen beyond, and then continue in this one state. But...

Greetings, I was wondering if anybody knew whether or not the moment of wavefunction measurement is always associated with a high energy. I know that we require smaller and smaller wavelengths of light to probe smaller distances, and since energy increases as wavelength decreases, I was...

Homework Statement A particle is described by the wave function psi(x) = b(a2-x2) for -a < x < +a and psi(x) = 0 for x < -a and x > +a, where a and b are positive real number constants. a) Using the normalization condition, find b in terms of a. b) What is the probability to find the particle...

Homework Statement Griffiths Intro Quantum Mechanics free particle question. Normalize wave function, find Phi(k), Psi(x,t), and comment on its behavior for small and large a. The wave function given is Ae-a|x|Homework EquationsThe Attempt at a Solution I found the correct Phi(k), but for the...

I now understand how the wavefunction graphs look from the hyperphysics: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hosc5.html. However, what I fail to understand, is how the wavefunction equation was derived for the 1st excited state, from: ground_wavelength0 = (a/pi)1/4 e(-ax2/2)...

I am curious, if I were to draw a wave function, would one for ground state and one for excited sate be different? If different, could someone explain how and why? If you could, thanks!

Homework Statement I was hoping someone could verify that I've set up the integral correctly for this problem.. Suppose that at t=0, the wavefunction of a free particle is ψ(x,0) = \sqrt{b} e^{-|x|b + ip_0 x/\hbar} a) what is the momentum amplitude for this wave function? Homework...

I've been a bit puzzled regarding the relation of the Schrodinger equation (SE) and the wave function, and what they mean. Here's kind of where I'm at. 1) I always thought that in the standard form of the SE, either the time dependent or independent form, that the wave function Psi (ψ)...

in the time-dependent schrodinger equation , our sir told us about energy and momentum operators . He just defined them , the equation was of the form Aexp(i(kx−ωt)) .if we take the equation of the form Aexp(i(kx+ωt)) will those operators change . if so generally for a wave how do we determine...

I have only ever seen the wavefunction for a spin 1/2 particle written in the basis set |α> |β>. I was interested in how a wavefunction |ψ> = a|α> + b|β> might be rewritten in a continuous basis and hence would need to know what the actual functions of |α> & |β> were. Thanks

The hypothesis that a conscious observer collapses the wave function has been discarded, right? The real reason is that the particle you use to measure the other disrupts the wave function, forcing it to choose an eigenvalue. So since we are able to remove the conscious observer as the...

This is Problem comes from Griffiths Quantum Mechanics textbook; specifically, it is problem 2.5 (b). A particle in an infinite square well has its initial wave function an even mixture of the first two stationary states: \displaystyle \Psi(x,0) = A[\psi_1(x) + \psi_2(x)] Here is the part of...

Hello everyone, this has been on my mind for a while and I finally realized I could just ask on here for some input :) I think in general, when most people start learning quantum mechanics, they are under the impression that the wave function \Psi represents everything you could possibly know...

Definition/Summary A wave function is a mathematical function that describes a physical system in quantum mechanics. The time evolution of this wave function, and thus of the system itself, is described by the Schrodinger equation. Equations P_G=\int_{G}\psi^*\psi d^3 x Schrodinger...

This was in my Introduction to modern physics exam, but i don't quite know what i should do here... My teacher said there was an easy trick. Can you guys help me? An electron is described by the following wave function ψ(x)=(ax+b for 0<x<L, cx+d for L<x<3L, 0 for x<0 V x>3L) a)...

Hi, I was wondering whether we are sure (I know, strong word) that decoherence is the mechanism that takes us from the quantum world to our classical world. Correct me if I'm wrong, but basically decoherence is a phenomenon where we have a bunch of quantum states that, when piled onto each...

Homework Statement Doing a bit of QM from Griffiths intro to QM and got stuck early on on the following worked example: http://imgur.com/6aPVGIr I was under the impression that the mod square of the wave function ψ(x,t) should always be a positive, real number, but I cannot understand...

Hello, I would like to understand why particle are caraterized by their wave funtion ? Why parameters are probabilisticly defined ? I see no contradiction, physics problem or mathématical reason to this. Is wave function is a fundamental hypothesis of quantum mechanic or there is a proof...

What is the "A" in the wave equation: Ae^{i(kx-wt)}? What does it mean in quantum mechanics? Is it just the amplitude?

I have read a number of books on quantum mechanics and I am now at peace with the idea that the wave-function of an electron instantaneously populates the universe with finite probabilities that the electron will be detected at a given point, if a measurement is conducted at that point. However...

Homework Statement Consider the wave function $$\Psi(x,t)=Ae^{-\lambda|x|}e^{-i\omega t}$$ Where ##A##, ##\lambda##, and ##\omega## are positive real constants. (a)Normalize ##\Psi##. (b)Determine expectation values of ##x## and ##x^2##. Homework Equations...

Am I right to think that particles cooled asymptotically to 0 K would have wave functions the size of galaxies or even larger (provided they would stay cooled long enough for that light cone---).

Does the measurement problem ("wave function collapse") or something similar somehow manifest itself in QED and other quantum field theories? Is it somehow built-in into the propagators etc. "away from sight"? If so, how does it affect the theories and is this a problem, which needs to be...

Hello! I am not quite sure how do i verify the complex wave function of EM wave \vec{E}(x,y,z,t)= \vec{E}0ei(kz-\omegat+\delta) is a function of the wave equation \nabla2\vec{E}=\frac{1}{c^2}\frac{∂^2E}{∂t^2}

Homework Statement Applly conditions to azimuthal wave function for an electron in the hydrogen atom to show that ml, the magnetic quantum number, can take on any integer value. See attachment for actual question. Homework Equations I'm pretty stuck, is it something to do with the...

Hi. I never understood why the momentum wave function ##\phi (p)## is the Fourier transform/integral of the real space wave function ##\psi (x)##. Basically, the second pair of formulas here http://quantummechanics.ucsd.edu/ph130a/130_notes/node82.html, and (and the rest of the text, for that...

I understand that a local gauge transformation functions to conserve the energy of an electron as it moves through space/time. What I don’t understand is why the energy of the electron, as dictated by the momentum and potential energy terms of the Schrödinger equation changes as a function of...

First of all note that 8-dinensional Finsler space (t,x,y,z,t^*,x^*,y^*,z^*) preserving the metric form \begin{equation} S^2 = tt^*-xx^*-yy^*-zz^*, \end{equation} actually presents doubled of the Minkowski space. Then the solution with one-dimensional feature localized on the world line...

Homework Statement If I have a wave function that goes to infinity can I assume that the derivative also goes to 0 at infinity? Homework Equations The Attempt at a Solution The reason I think it does is because the wavefunction and its derivative must be continuous everywhere...

¿Is there an unique wavefunction for a system if we know the distribution probability function for variables from the system and first derivatives from these variables and we have the gauge fixed (by external impositions not related with the wavefunction knowledge obviously? (Nothing about...

I have these questions on the exam after three days I do not know how to solve Please help me http://im57.gulfup.com/qzZrpe.jpg http://im57.gulfup.com/7lwZaV.jpg http://im57.gulfup.com/FCHM55.jpg