Hi all,
How do we find the eigenfunctions if we are given the wavefunction? I have a wave function at time = 0 and it is of a *free* particle and I need to find the wave function at a later time t. I did :
\Psi(x,t)=\Psi(x,0)*e^{-iHt/hbar} then
\Psi(x,t)=\sum_{n}(<\phi_{n}|\Psi(x,0)>...
Hello,
How do I find the normalization constant for psi(x,y,z) = N exp -(x/2+y/2+z/2) ??
I did the following:
\int(psi^* psi)dx dy dz = 1
the integral bounds are from -infinity to infinity and the * means the complex conjugate.The integral is so weird that I couldn't find N. I used...
Homework Statement
At t=0, the particle is in the eigenstate S_x , which corresponds to the eigenvalues -\hbar \over 2 The particle is in a magnetic field and its Hamiltonian is H=\frac{eB}{mc}S_z . Find the state at t>0.
Homework Equations
Eigenstate of the Sx is...
Homework Statement
Find the momentum-space wave function, \Phi (p,t), for a particle in the ground state of the harmonic oscillator. What is the probability (to 2 significant digits) that a measurement of p on a particle in this state would yield a value outside the classical range (for the...
I need to normalize the following wave function:
psi= Cexp(-abs(x))exp(-iwt)cos(pix)
I know that when squaring it, the time dependent part drops out, which is good, but what I seem to be left with is
Psi^2=C^2exp(-2abs(x))cos^2(pix)
Which seems like a fairly complicated integral to...
Hi all, I've got a question I think I understand conceptually but not mathematically...
Homework Statement
A transverse sinusoidal wave on a string has a period T = 25.0 ms and travels in a negative x direction with a speed of 30.0 m/s.
At t=0, a particle on the string at x=0 has a transverse...
I want to know whether the wave function of particle is unique? If not, could we find a ψ to rationalize the equation Pψ=Aψ, in which P is the momentum operator and A is a constant. Thank you!
XXZ model in 1-dimension, with external field, what is the exact form of its ground state wave function? Recently I've read the ground state wave function of XY model and was curious about the condition of XXZ. Do they have a similar manner?
The XY result is attached below.
Thanks.
Homework Statement
Hi all, I've been given some homework on wave functions to find direction and velocity etc... but as its the first week of uni for me, we haven't even covered wave functions or anything :/ and the homework is due on weds 10th oct...
Homework Equations...
I've heard some people say that the wave function and its first derivative must be continuous because the probability to find the particle in the neighborhood of a point must be well defined; other people say that it's because it's the only way for the wave function to be physically significant...
Homework Statement
Just a snipit of one of my homework problems. I'm trying to find out what \Psi \frac{\partial \Psi^{*}}{\partial x} equals to help me find out what the probability current for a given free particle is.
Homework Equations
\Psi = Ae^{i(kx-\frac{\hbar k^{2}t}{2m})}...
Why is it that when observing an electron or photon it causes the wave function to collapse, surely the photons that cause this collapse were still "colliding" with it when we wern't looking. Or does it only collapse the wave function from the observers viewpoint?
(I'm abit of a noob so if...
Uncertainty - Harmonic Oscillator
The Wave function for the ground state of a quantum harmonic oscillator is
\psi=(\alpha/\pi)^{1/4}e^{-\alpha x^2/2}
where \alpha = \sqrt{ mk/ \hbar^2} .
Compute \Delta x \Delta p known:
Heisenberg Uncertainty Principle:
\Delta p \Delta x >= \hbar/2...
Hi...I am new to this forum.
Can somebody clear a fundamental doubt i have?:rolleyes: A wave function has a form found by applying Schrodinger's equation. In steady-state systems, arent the system eigen functions, the wave equation of the system? if so is it the energy eigen function or the...
Hi,
I'm looking at this wave function:
\psi(x,t) = \frac{4}{5}{\psi}_{1} + \frac{3}{5}{\psi}_{2}
The functions involved here are the typical eigenfunctions for the ground state and first excited level in an infinitely-deep 1-D square well.
Defining
A = 4/5.\sqrt{2/a}
B =...
Is it correct to think, that with a scalar complex Klein-Gordon field the wave function \Psi:\mathbb{R}^3\to\mathbb{C} of one particle QM is replaced with an analogous wave functional \Psi:\mathbb{C}^{\mathbb{R}^3}\to\mathbb{C}? Most of the introduction to the QFT don't explain anything like...
A wave function (psi) equals A(exp(ix)+exp(-ix) in the region -pi<x<pi and zero elsewhere.
Normalize the wave function and find the probability of the particle being between x=0 and pi/8
Equation is : the integral of psi*(x,t)psi(x,t)=1 for normalization
Homework Statement
I have a problem in which I have a two-atomic molecule, and I'm supposed to find the energy and wave function in the ground state, given the particles' masses m_1,m_2 and the potential V(r)=kr^2, where r is the distance between the particles.
I don't necessarily need this...
Homework Statement
phi(r,0)=1/rt(2)(phi1+ph2)
What is phi(r,t)?Homework Equations
The Attempt at a Solution
Is this simply a case of introducing a phase constant to the eqn. So:
phi(r,t)=1/rt(2)(phi1+phi2)e^i(theta)t
or do we need to modify phi1 and phi2.
Hi!
How can I write the wave function of a particle in an infinite box (in the state n) as a superposition of the eigenstates of the momentum operator?
the wave function is:
PHIn(x,t) = sqrt(2/a) * Sin(n * PI/a * x) * exp(-i En/h * t)
Thanks for your help!
If I have af wavefunction that is a product of many particle wavefunctions
$\Psi = \psi_1(r_1)\psi_2(r_2) ... \psi_n(r_n)$
If I then know that the parity of $ \Psi $ is even. Can I then show that the wavefunction i symmetric under switching any two particles with each other. That is...
Homework Statement
Use the ground-state wave function of the simple harmonic oscillator to find: Xav, (X^2)av and deltaX. Use the normalization constant A= (m*omegao/(h_bar*pi))^1/4.
Homework Equations
deltaX=sqrt((X^2)av-(Xav)^2)
wavefunc=A*e^(-ax^2) ?
The Attempt at a...
Hello
I know that every particle has attached a wavefunction in quantum mechanics.
How does a free particle move in quantum mechanics?
The wavefunction has periodic zeroes, and the |wavefunction|^2 gives the probability of finding that particle...so does this mean that in space the...
I have a couple questions about finite potential barriers that I can't seem to figure out on my own...
1) Why does the real part of the wave function collapse inside the barrier (square, rectangular, barrier with V less than the energy of particle)? It seems to me that there should be some...
Homework Statement
While solving the integral of a wave function,I came across the term cos(n*pi) , where n is an integer. Is that term equal to +1 or -1 (I know that it could be either one depending on whether n is odd or even) but how do I proceed with the integral?
Homework...
"(a) Use the radial wave function for the 3p orbital of a hydrogen atom (see Table 15.2) to calculate the value of r for which a node exists.
(b) Find the values of r for which nodes exist for the 3s wave function of the hydrogen atom."
For part a, I looked at Table 15.2 and found the equation...
I am just learning QED and could not understand the role of wave function. Is the basic equation in QED the Schrodinger Equation? Is the difference between Quantum mechanics and QED just they have different Hamiltonians.
I have tried to read the original paper of Tomonaga in 1946 Progress of...
what would a wave function of
phi(x) = Ke^(-a|x|)
look like?
would it be like an exponential graph with a graph reflected along the y axis?
and its probability distrubution (phi)^2?
i have no idea...i can't seem to find it by googling.
Hi all,
I've got a tough problem that I need some guidance on.
Question: Consider a wave function that is a combination of two different infinite-well states, the nth and the mth...
we often say that the square of wave function gives us the probability density where the particle is. how can the square of a function might predict about the existence of a particle?
Question from textbook (Modern Physics, Thornton and Rex, question 54 Chapter 5):
"Write down the normalized wave functions for the first three energy levels of a particle of mass m in a one dimensional box of width L. Assume there are equal probabilities of being in each state."
I know how...
When doing the initial conditions of the velocity of the wave function, why do they have a position (x) derivative (i.e. cF'(x)-cG'(x)=h(x)).
It appears in here.
http://en.wikipedia.org/wiki/D%27Alembert%27s_formula
How someone explain how the c came about and why position derivatives are...
I found a layman's explanation of the wave characteristics of subatomic particles in the form of a "Dr.Quantum" video from "What the Bleep do we know?". Aside from the parapsychological junk in the last 2/3rds of the movie, the explanations of quantum properties seemed mostly accurate and...
A wave function psi = 3i|up> + 1|down> corresponding to the spin of the electron.
If I want to draw the distribution of the measured outcome, do I do the following?Probability of spin up = 0.9
Probability of spin down = 0.1
So I would draw a bar graph showing that spin up has a value of 0.9...
I solved the differential equation for theta portion of the hydrogen wave function using a power series solution. I got a sub n+2 = a sub n ((n(n+1)-C)/(n+2)(n+1)). I then truncated the power series at n = l to get
C= l(l+1).
I know need to use the recursion formula I found to find the l =...
how fast does the wave function "decollapse"?
as you know the wave function (indeterminacy) may collapse due to a measurement. However, after a measurement it returns after a while to its initial state of indetermincy. (I don't know what to call this transition back to indetermincy; is there a...
The following is a "ooze" wafve function:
\Psi_{ooze} (x,t)=\frac{1}{K} \left( \Psi_1 + \Psi_2+...+\Psi_{1000} \right)
1. I am to find the value of K, but I don't even know what it represents. Is K the coefficent to normalize the probablity to 1?
2. Probability where energy E_q...
I'm having problem with griffith QM problem 4.43:
Construct the spatial wave function for hydrogen in the state n = 3, l =2, m = 1. Express your answer as a function of r, \theta, \phi, and a (the Bohr radius) only.
My prof. gave hints about radial wave function, but I have no idea how to...
the wave function descrbing a state of an electron confined to move along the xaxis is given at time zero by:
\Psi(x,0)=Ae^{\frac{-x^2}{4 \sigma^2}}
where sigma is a constant (i believe).
I am asked to find the probability of finding the electron in a degion dx centered at x=0.
I...
My intuition is that it would be unitless. But if it's magnitude squared is a probability density, then its units would have to be 1 over some power of length. Specifically 1/L^(n/2) where n is the dimension. Where's the error in my thought? Thanks
Hello. In QM we can determine the probability of any event ocurring given the wavefunction. Once we actually take a measurement the particle 'picks' a state to be found in.
so my question is how do we know a priori that the particle is in two or more states at the same time before we make a...
how do you find the normalized wave functions of the hydrogen atom for n=1, l=0 and ml=0?
in my textbook, it's a table, but i have no idea where the figures come from...
why does the wave function have to be normalizable, and why does it have to go to 0 and x approaches positive/negative infinity and y approaches positive/negative infinity ?