Wave function Definition and 865 Threads

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.

Hello! Can somebody tell me, how it is possible to normalize the wave function of a free particle using the Dirac delta function? Thanks!

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*omega[SIZE="1"]o/(h_bar*pi))^1/4. Homework Equations deltaX=sqrt((X^2)av-(Xav)^2) wavefunc=A*e^(-ax^2) ? The Attempt at...

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...

In quantum mechanics, why is a wave function not normalizable if it always has the same sign as its second derivative?

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...

I think it needn't be continuous even if the probability should. Wave function can be complex while probability is its absolute value.:bugeye:

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...

[FONT="Comic Sans MS"] 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...

Whats the relationship between the wave function and the uncertinaty principle? if there's any thanks

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 it equal R(r)cita(cita)phi(phi)?

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 ?

What does it mean by "shot wave length corresponds to high curvature of the wave function" ?

Scientists wan't to know where wave function collapse occures. I have found at least one. Take the experiment of shooting electrons through two holes that are close together and seeing where they land at a detection screen on the other side. If you shut one hole you get a particle or lump...

I need to explain why, as the energy of a bound state in a finite potential well increases, the wave function extends more outside of the well. I need to do this from both a mathematical and a physical point of view. I think I know the mathematical explanation (see attached image). Can anyone...

for the following question: the wave function of a moving particle (a) reflects the probablity of finding the particle at a particular place and all the time (b)reflects the probablity of finding the particle at a particular place and a particular time (c)reflects the probablity of finding the...

I didn't find an article about this so I'll ask it here: How does the quantum mechanical wave function of a particle arise in ST? Sorry if it has been asked before, but I couldn't find a topic about it.

Normalization of a wavefunction Let Phi be a wave function, Phi(x)= Integral of {exp(ikx) dk} going k from k1 to k2 I'm having trouble normalizing the wave function. I calculated the integral, then multiply by its conjugate and now I'm supposed to integrate again /Phi(x)/^2 in all...

Hey! Here is one that I thought would be easy: Two traveling waves move on a string that has a fixed end at x=0. They are identical except for opposite velocities. Each has an amplitude of 2.46mm, a period of 3.65ms, and a speed of 111m/s. Write the wave function of the resulting standing...

A short question: I've learned that the wave function corresponding to a free particle has this form: Psi(x,0)=1/sqrt(2*Pi)*Integral[g(k)*E^(ikx)dx] (i can't write it in Latex, sorry) Is it just for the free particle, or any quantum state of a system can be represented in this form...

The Second Ring of Life; The Vesica Attractor by Christopher Humphrey Abstract The fossil record shows a disparity in the formation of complex body plans. The individual eukaryote cannot build these structures. They do not carry within themselves a blue print for an overall structure...

i am having difficulty with the wave function. for example in the exercise we are told to write the expression : a cos x+ b sin x in the form k cos(x-a) This i had little problem with and was able to work out what quadrant i shoul use etc what i mean is the all positive. sin positive...

Hey, if anyone can throw in some thoughts I am a little lost. Not sure If I need to integrate, or what. Thanks for any help. The wave function for a hydrogen atom in the 2 s state is:(attachment) I need to Calculate the probability that an electron in the 2 s state will be found at a...

What if complex biological systems emerged as a result of a wave function firstly, and the biochemical components followed after. Can this new perspective better explain organizational gaps in evolution. The Phi-Wave Aether: a Wave Theory of Everything Caroline H Thompson...

Hey. I am pretty confident i have solve this problem. I just solve the integral of the given wave function, with the given limits... However, I am having a difficult time integrating it. The sqrt(2/L) can be brought outside of the integral, but what can i with the sin function? The wave...

Hi, I have a question about the mathematical requirements of a wave function in a potential that is infinite at x \leq 0. (At the other side it goes towards infinity at x = \infty.) Now, given a wave function in this potential that is zero for x = 0 and x = \infty. Does it matter what that...