Wave function Definition and 878 Threads

Hi everyone, Assume that we have an electron in the Coulomb field of a proton, whose wave function is specified. How can I find the probability of finding this electron in the ground state of the hydrogen atom? Thank you.

Homework Statement A problem from an examination: A hydrogen atom is in the state \Psi=A(\sqrt{6}\psi_{100}+\sqrt{2}\psi_{200}+\psi_{211}+2\psi_{31-1}+\sqrt{3}\psi_{321}+3\psi_{32-2}) where \psi_{nlm} are the eigenfunctions of hydrogen. Find A so that the equation is normalized. Homework...

Hi, I have a few question about orbitals 1. What does psi or wave function represents? 2. When talking about orbitals what does phases actually mean (does it relate to charge and electron spin)? 3. What's the mechanic behind when phases cancel out to create sigma*1s antibonding...

Hi, I am new here. I am a graduate student of department of physics at some university in Korea. If there is any wrong in my english, I will apologize in advance. I am preparing for my qualifying exam that is going to be held on next month. Homework Statement The question is very simple as...

Homework Statement One wave function of H like atom is \psi=\frac{\sqrt{2}}{81\sqrt{\pi}a_{0}^{3/2}}(6-\frac{r}{a_{0}})\frac{r}{a_{0}}(e^{\frac{-r}{3a_{0}}})cos \theta How many nodal surfaces are there? 1)1 2)2 3)3 4)none of these The Attempt at a Solution Its an objective...

A wave function(psi) is a mathematical quantity which gives complete information about the state of a system at a particular instant of time. But what information does the complex conjugate of a wave function(psi*) give? Does it represent the same state as psi? Or does it just have a...

Homework Statement \psi_{n}(\theta)=A_{n} \exp(\imath n \theta) where n is an integer Calculate the factor A_{n} if the wave function is normalized between \theta = 0 and \theta = 2\pi. Homework Equations NA The Attempt at a Solution 1=\int_0^{2\pi} |\psi_{n}(\theta)|^2...

hello all

what is a wave function? And how do we define a wave function? How is it related to schrodinger's equation?

A transverse sinusoidal wave on a string has a period of 25 ms and travels in the negative x direction with a speed of 30 m/s. At t=0, a particle on the string at x=0 has a displacement of 2 cm and is traveling downward with a speed of 2 m/s. Find the amplitude, phase constant, and maximum...

Homework Statement A system's wave function has the form \psi(r, \theta, \phi) = f(t, \theta)cos\phi With what probability will measurement of L_z yield the value m = 1? Homework Equations L_z|\ell, m> = m|\ell, m> The Attempt at a Solution I feel like there may be a typo...

The Perimeter Institute has a talk on the Feynman chessboard / checkerboard model scheduled for a few days from now. This will be recorded and you can play it back, sometime after November 18th. Links: Speaker(s): Garnet Ord - Ryerson University Ord's website...

I was reading part of a book which was explaining about the probability of finding a particle on a 1d line. \int^{+\infty}_{-\infty}P(x) dx = 1 This sounds right because if the line was infinitely long then the particle must be on it. You can them intergrate between a and b to find the...

Homework Statement a particle moving in one dimension between rigid walls separated by a distance L has the wave function \Psi(x)=Asin(\Pix/L), since the particle must remain between the walls, what must be the value of A? Homework Equations The Attempt at a Solution Ok so I'm...

As far as I understand it, an electron exists as a probability cloud around an atom, representing all the possible places it could be. Then when we make an observation the wave function collapses to one point where we see the electron. So what happens if we keep looking at it? Does the elctron...

Homework Statement Knowing: y(x,t) = Acos(kx-ωt) Find the partial derivatives of: 1) dy/dt 2) dy/dx 3) d^2y/dt^2 4) d^2y/dx^2 Homework Equations The Attempt at a Solution These are the answers the actual answers: 1) dy/dt = ωAsin(kx-ωt) = v(x,t) of a particle 2) dy/dx =...

the double slit experiment is explained in QM as the superposition of two wave functions. Each is the wave function for one of the slits. an electron starts out with a wave function that is clustered near the point of emission and then evolves on some way according to the Shroedinger...

Homework Statement Hi guys, I'm really confused about how to about solving this problem, any help would be much appreciated. Consider the wave-function: \Psi(x,t)=\left\{\begin{array}{cc}Asin(pi*x)\exp^{-it\omega},&\ -1\leq x\leq 1\\0, & \ elsewhere\end{array}\right{ a) Determine A...

Here's the sitch: I am given an equation, A*e-a(mx2/h-bar+it) I need to find the value for A that will satisfy normalization, as well as find the Potential of the Schrödinger Equation using this value. What do I do? P.S. I have NOT learned gaussian integration, which is where I run...

Homework Statement Come up with a wave function Psi[x] that satisfies the given known values: <x>=-1 sigma x = 1 <p> = h bar Homework Equations The Attempt at a Solution So far I have this equation, which satisfies <x>, <p>, but not sigma x. 1/[Pi]^(1/4) E^(i (x + 2)) E^(-(1/2)...

Homework Statement Hi all. I have a wave function given by \Psi \left( {x,0} \right) = A\frac{x}{a} I have to normalize it, which is OK. But in the solution to this problem, the teacher uses |A|2 when squaring A. Is there any particular reason for this? I mean, if you square the constant...

Homework Statement Check that a given momentum space wave function is normalized. I've done the integral, but the result is not dimensionless. Here is the wave function: \overline{\phi} = \frac{1}{\pi} ( \frac{2 a_{0}}{\bar{h}})^{3/2} \frac{1}{(1+(a_{0} p / \bar{h})^2)^2} The units of this...

I believe it does, but I'm having a debate with someone and I'm trying to prove why the universe must have a wave function. I was under impression the best equations for describing our universe involve it having it's own wave but he's asserting it doesn't need one. Can anyone help me? Super newb...

I believe it does, but I'm having a debate with someone and I'm trying to prove why the universe must have a wave function. I was under impression the best equations for describing our universe involve it having it's own wave but he's asserting it doesn't need one. Can anyone help me?

What is exactly a wave function of the system. I have been told that wave function is something that is used to describe the wave nature of a particle but how? I could not understand or rather visualize it. And how can the wave function be a complex number or a negative value? For example if...

what is it that actually collapses a wave function, an observer? what constitutes an observer? also is it true that everything has a wave function, because if it does who collapsed the universes wave function some may say wave function collapse only works on the quantum level but the universe...

Hi, I've been working on writing the wave function in terms of momentum eigenfunctions. The only problem I have with the derivation is the last step, which allows me to write: \Psi(x) = \int^{\infty}_{-\infty} \phi(p)u_{p}(x)dp where u_{p}(x) =...

Its looking quite simple problem but let me explain properly my question. Wave function as we know is also known as matter wave/field amplitude. Then definitely there is associated a wave with it. Then how can we say that wave amplitude vanished at infinite!

Problem We have the function g(x)=x(x-a) \cdot e^{ikx}. Express g(x) in the form \sum_{n=1}^\infty a_n \psi_n (x) where \psi_n = \sqrt{\frac{2}{a}} \sin \(\frac{n\pi x}{a}\) Solution I have absolutely no clue as to how to start... I know a bit about Fourier series, but here, the...

how to tranform wave function(x,t) to same coordinate wave function(x',t') with Lorentz Tranformation (please show all the calculus). and why we know the Lorentz tranform can do this function to use in every inertial frames.

Homework Statement Does the wave function have a dimension? If it does, what are the dimensions for 1D and 2D box problems?Can you generalise this to n dimensions? Homework Equations The Attempt at a Solution Yes, it does have dimensions. For 1D box it's [tex] m^{-2} [tex]...

Hi, could someone please tell me how I would show that a wave function is correctly normalised? I know to integrate the square of the function between infinity and negative infinity, but is the complex conjugate required? Any help is much appreciated :D

Hi everyone, Can anybody solve my simple problems of quantum: Usually we say, that wave function Ψ is dependent on r,θ,Φ .But this is just a coordinate system,or more than that. Imagination to this is qite difficult. Moreover somewhere in a book I have read that if Ψ = f(r,θ) exp(imΦ),then on...

Homework Statement A particle of mass m is in the ground state of the infinite square well. Suddenly the well expands to twice its original size, the right wall moving from a to 2a- leaving the wave function (momentarily) undisturbed. The energy of the particle is now measured. What will be the...

I read in my textbook that the wavefunction of a particle evolves causally when unobserved. but isn't it constantly being observed or detected in some sense by its gravitational effects?

Homework Statement I am having a problem with an example problem in my physics book. The example goes like so: a.)Show that \psi(x) = Ax + B A, B, constant is a solution of the Schrodinger equation for an E = 0 energy level of a particle in a box. b.) what constraints do the boundary...

Does anyone know how to construct a Time-independent wave function with given energies and probability on obtaining energies.

Homework Statement Construct wavefunction with given energies and probabilities of obtaining energies in a 1-D box from 0 to aHomework Equations [b]3. The Attempt at a Solution I know the general form of a time-independent wavefunction but I don't know what to do with the probabilities of...

For a particle in a 1-dimensional box confined by 0<x<a. a)Construct a wave function phi(x)=psi(x,t=0) such that when an energy measurement is made on the particle in this state at t=0, the following energy values are obtained with the probabilities shown: Energy E_n Obtained ...

Hi, Suppose there is half-half a mixture of an electron gas and a gas of some hypothetical particle with the same mass, spin but an opposite charge (like positrons that don't decay). Would anyone be able to tell me how the Slater determinants combine in this case? The HF wave function for just...

Can a quantum wave function be infinite at a point? For example you could have a radially symmetric wavefunction that's infinite at the center, yet the integrated probability is 1. Is this unphysical somehow? Laura

[SOLVED] Wave Function Solution Homework Statement An electron is found to be in a state given by the wave function http://rogercortesi.com/eqn/tempimagedir/eqn7955.png Find the value of A. Homework Equations The normalization of the wave function...

[SOLVED] Probability Current for Free Particle Wave Function Homework Statement Find the probability current, J for the free particle wave function. Which direction does the probability current flow?Homework Equations J(x,t) = \frac{ih}{4\pi m}\left(\Psi \frac{\partial \Psi^{*}}{\partial x} -...

does a phase factor (that can be represented by an imaginary exponential) in psi (the wave function) really matter? I am doing a problem and getting an answer that looks like sin[n(pi)x/a] when the answer is actually sin[n(pi)x/a-n(pi)]. I am just wondering at all if it makes any defference in...

Homework Statement Show that y(t-x/v) is a solution of the wave equation without taking any partial derivatives (hint: use your knowledge about f(x-vt)). Homework Equations y(x,t)=y(x-vt) The Attempt at a Solution what exactly is y(t-x/v) means, from dimension analysis, its the...

hello I am just starting some revition for my exams and havr come across this wave funchion and i don't no how to normerlise it i really need some help with this. it is the wave function symbol (x) = -Ae^(σx^2/x^2) what i need to know is how to intergrate it to find a value for A to see if...

Reading Sam Treiman's http://books.google.de/books?id=e7fmufgvE-kC" he nicely explains the dependencies between the Schrödinger wave equation, eigenvalues and eigenfunctions (page 86 onwards). In his notation, eigenfunctions are u:R^3\to R and the wavefunction is \Psi:R^4\to R, i.e. in contrast...

I have a wave function problem that I need to figure out... I have a really borderline grade, so it could mean the difference between an 'A' and a 'B' in my graduate Modern Physics class. Basically, I have to figure out the wave function and the transmission and reflection coefficients. My...

Homework Statement P = \int_a^b \, \left| \psi(x) \right|^2 \, dx If the particle in the box is in the second excited state (i.e., n=3), what is the probability P that it is between x=L/3 and x=L? To find this probability, you will need to evaluate the integral: \int_{L/3}^L...

Homework Statement Open Question 2.bmp Homework Equations The Attempt at a Solution Open Answer 2.bmp I really struggled with this one, my answer is nothing more than an incomplete educated guess.