Wave function Definition and 878 Threads

The 1s radial function of the wave function of H atom is: R10=2 a-3/2e-r/a ,where a = 5.29*10-11 meter but substituting a with its value,we will get R10 = 5.2*1015 *e(-1.89036*1010 r) and that is impossible if r=a and R(r)=1.9*1015 where is the problem ? What's more, the unit...

dimensions of the one-dimensional wave function? is it [si]=L-1/2?

Homework Statement "A wave function is given by Aexp[(-x2)/(2L2)] with an energy of E = h-bar2/2mL2. Assuming this is a solution to the time-independent Schroedinger equation, a) What is V(x)? Make an accurate sketch of V vs. x with labeled axes b) What sort of classical potential has...

Ok so from my understanding, the wave particle duality of matter is simply the fact that matter sometimes behaves as a wave and sometimes behaves as a particle. Ok, but I wonder if this has anything to do with the wavefunction. The wave function gives us the probability spread of matter at any...

I am given the following: A spherically propogating shell contains N neutrons, which are all in the sate \psi(r,0)=4\piij_{1}(kr)(3/\sqrt{34}Y^{0}_{1}+5/\sqrt{34}Y^{-1}_{1}) at t = 0. How do we find \psi(r,t)? My attempt: I have a few thoughts; could you apply the...

Homework Statement The wave function \psi_0 (x) = A e^{- \dfrac{x^2}{2L^2}} represents the ground-state of a harmonic oscillator. (a) Show that \psi_1 (x) = L \dfrac{d}{dx} \psi_0 (x) is also a solution of Schrödinger's equation. (b) What is the energy of this new state? (c) From a look at...

Homework Statement Find the ground state wave function for the 1-D particle in a box if V = 0 between x = -a/2 and x = a/2 and V = \infty Homework Equations I would guess -- Schrodinger's time-independent equation...

Homework Statement How does the wave function of spin 1/2 change under parity? Homework Equations The Attempt at a Solution The behavior of the eigenfunctions of orbital angular momentum L is easily seen from their explicit form, namely spherical function Yml is multiplied by...

Hi. I have a simple question- Does the wave function describe probability of finding a particle in a certain state upon collapse of the wave function?

N.B. I am not trying to send information back in time or generate infinite free energy (also I couldn't find how to delete the other thread but could a moderator please delete it for me) If you could send classical information signals faster than light, then according to relativity you could...

Okay, so I am no expert in this field, but would like to acquaint myself more with quantum mechanics. As I understand it, the collapse of the wave function according to MWI only appears to occur, when really the observer is copied into as many different histories or worlds as there are possible...

Homework Statement Calculate the probability of finding the electron in a hydrogen within the angle \pm30\circ from the x-y plane.The hydrogen is in the (2,1,1) state. Homework Equations probability = \int\int\int\left|R_{2,1,1}\right|^{2} \left|Y^{1}_{1}\right|^{2} r^{2} sin(\theta) dr...

I was wondering if this is correct: \phi(k-a)=\phi(k)-\phi(a) Where k=p/h (h bar that is) and a is some constant and \phi is the Fourier transform of a wave function (momentum function). I know that if I had some real formula for \phi I could just test this but the problem isn't like...

Radial Wave Function; Normalized Radial Wave Function 5. Is the brute-force method the only way to show the Equation is satisfied? By that I mean differentiating R20 once, twice, and substituting it in? I tried that earlier, but it was very nasty...

Have Zernike Polynomials ever been applied to Schrondinger's Equation instead of psi? They're widely used in optics and seem to offer comparable positive traits. http://en.wikipedia.org/wiki/Zernike_polynomials http://wyant.optics.arizona.edu/zernikes/zernikes.htm

Lets say we have a system in a 1D infinite potential well, prepared somehow with the wavefunction: (phi)=C(a-x)x. I understand that if I try to measure the system's energy, I will collapse the system to an eigen state ((psi)=Asin(n pi x/length)+Bcos(n pi x/length)), returning an eigen energy...

Homework Statement Here are the screenshots of the textbook... http://i37.tinypic.com/nce7md.jpg http://i36.tinypic.com/8zpwew.jpg What I don't understand is the parameter (x - vt) I am confused by the picture. This is why I can't even ask a precise question, and rather I can only...

Homework Statement wave function of a particle in one dimension wave function of a particle in one dimension at time t=0 given by psi(x,0) = A(x^0.5)*(e^-ax) for x>0 or x=0 psi(x,0) = 0 for x<0 where x is in nms and a = 1nm where is the particle most likely to be found? or for...

Imagine an infinite, positive, uniform sheet of charge with a pinhole in it. A negative particle oscillates back and forth through the pinhole and in the +-x direction. The magnitude of the force on it is constant in time (although the force reverses direction when the particle passes through...

What I know: In stationary states the time dependence is factored out so it is of the form phi(q) * e^(-i omega t), thus in its appearance there is no wave function spread. However I recall from texts that wave packet spread is considered a universal phenomena in quantum mechanics, so I am...

What are solutions to \psi''(x) = (a_0 + a_1 x)\psi(x) ? First idea I've had was that I could try some kind of perturbation with respect to the a_1 variable, so that \psi(x) = A_1e^{\sqrt{a_0}x} + A_2e^{-\sqrt{a_0}x} + \psi_1(x) would be an attempt. But I couldn't find...

I'm still wrestling with the whole uncertainty principal / wave function collapse idea. Obviously a basic building block of QM, I'm having a hard time understanding the real world evidence which supports these QM piles. 1. So from my understanding, the uncertainty principle tells us it is...

I have books (Quantum Theory by Bohm for example) with derivation of the spread of the wavefunction of a free particle in the Schrodinger equation. But does this spreading only happen as a free particle? What about under the general Schrodinger equation where there exist potentials that seem to...

I think that the wave function is the description of a particle's position at a point in time. But I'm not precisely sure what an eigenfunction is and how it is different. I know that certain eigenfunctions return certain values, and that even if you do not have a certain eigenfunction you can...

Hi. I've asked the question many times (as I'm sure many others have) why does the particle behave differently once it has been observed? Does that not mean it knows it has been observed? How does it know? The only answer I get is: "observing destroys the wave function" , but that doesn't...

Homework Statement Find the expectation value of x (Find <x>) given the wave function: \psi(x)=[sqrt(m*alpha)/h_bar]e^[(-m*alpha*|x|)/(h_bar)^2] This wave function represents the single bound state for the delta-function potential. It's the solution to the shrodinger equation given the...

b]1. Homework Statement [/b] I have the soloution to this question, but am confused as to what has been done between each step between lines 2,3,4. Can anyone explain how they have been simplified (espicially what happened to the operator) and what the value of the intergral is? I think I am...

I want to know how to normalize symmetric and anti-symmetric wave functions ??

It is my understanding that a measurement of S_z followed by a measurement of S_y will result in a particle which is in an eigenstate of S_y . But it appears that a measurement of say S_y followed by a measurement of S_x results in zero. I see this from a question in which I am asked to...

At time = 0 a particle is represented by the wave function \Psi(x,0) = \left\{ \begin{array}{ccc} A\frac{x}{a}, & if 0 \leq x \leq a, \\ A\frac{b-x}{b-a}, & if a \leq x \leq b, \\ 0, & otherwise, \end{array} \right where A, a, and b are constants. (a) Normalize \Psi (that is, find A, in...

Wave functions are, of course, almost always complex-valued. In all of the examples that I have seen (infinite square well, etc.), the real part of the wave function and the imaginary part of the wave function are basically the same function (except for a phase difference and possibly a sign...

hello i attached my question if i can get some help i think that there is another way to solve this problem

Hello, I'm new to Physics Forums, so I apologize if this question seems somewhat uninformed, but I have recently started studying quantum mechanics, and was curious about the idea of the wave function collapse, and how, from what I can tell, it seems to be approached completely independently...

Homework Statement Demonstrate that if u_1 and u_2 are solutions of the wave equation \frac{\partial ^2 u}{\partial t^2} - \triangle u=0 such that u_1 (0,x)=u_2(0,x), \partial _t u_1 (0,x)=\partial _t u_2(0,x) and such that the difference "tends to 0 at infinity" sufficiently quickly, then...

Homework Statement Suppose that a hydrogen atom is in the 2s state. Taking r = a0, calculate value for \psi2s(a0) Homework Equations I did spherical harmonics for l=0 ml=0 times the radial wavefunction for n=2 l=0. Got the same thing as the solution manual attached but when I started...

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. Normalize \PsiHomework Equations \int |\Psi(x, t)|^{2} dx = 1 |\Psi(x, t)|^{2} = \Psi^{*}\PsiThe Attempt at a Solution I have a model solution -...

Homework Statement Using time independent 1D Shrodinger equation, show that if V(x) is even and Psi(x) is a solution, Psi(-x) is also solution. Then, assume Psi(-x) and Psi(x) differ only by a constant, show that the constant is either +1 or -1. Homework Equations The Attempt at a...

Homework Statement The function \Psi(r) = A(2-{Zr\over a})e^-{Zr\over 2a} gives the form of the quantum mechanical wavefunction representing the electron in a hydrogen-like atom of atomic number Z when the electron is in its first allowed spherically symmetric excited state. Here r...

Homework Statement http://www.ph.qmul.ac.uk/~phy319/problems/problems1.doc" Question 2)b The Attempt at a Solution http://img685.imageshack.us/img685/9033/p270210111001.jpg Is this correct? Thanks!

Homework Statement i. Confirming the wavefunction is normalised ii. Calculating the expectation values: <\hat{x}> , <\hat{x^{2}}> , <\hat{p}> , <\hat{p^{2}}> as a function of \sigma iii. Interpreting the results in regards to Heisenberg's uncertainty relation. Homework Equations...

Hi, I built a small program to show that the normalized hydrogen wave function (ground state) integrates to unity, as expected. But I got an absurd value: 4.6x10^19 instead. I spanned a big volume (30 Bohr's radius) calculating and summing the product dr*dphi*dtheta * psi * psi. Worse yet...

shai n and shai m are mutually orthogonal ...where n and m can any numerical value...but i can't imagine it how they can be perpendicular to one another ... (to me the worst thing is to think shai4 and shai100 are perpendicular) and what is the advantage or reason of it...can anyone help me to...

Homework Statement http://img29.imageshack.us/img29/5236/phst.jpg Homework Equations http://img25.imageshack.us/img25/8815/11203939.jpg I need to find the equation for the question. The Attempt at a Solution a) A bunch of waves/wave functions, that have phases/amplitudes that interfere...

If I understand correctly, a measurement affects the wave function only at the moment of measurement. In other words, if one were able to compare two wave functions, one when there were measurements, and one in which there were no measurements, the only difference would be at the meager set of...

Hello I need to calculate <x> (x is the location of neutron) and the state is and the integral is: Can I move the x to be near the integral symbol? and how to I multiply the matrices? And is this true: Can I move the psi to be near the psi*? And psi*x psi =psi^2=1 right? thanks

Fact 1.From relativity we have come to view the universe as 4 Dimensional. That is 3 Dimensions of space and 1 of time. As such I have the following questions. Questions 1. Given the universe is 4D, does it not follow that all objects within the universe is 4D? 2. If 1 is true, does it mean...

Homework Statement It's not a homework problem. I'm reading my textbook (Sakurai's Modern QM), and I'm not sure about a step (eq 3.6.6 through 3.6.8). Here it is: We start with a wave function that's been rotated: \langle x' + y' \delta \phi, y' - x' \delta \phi, z' | \alpha \rangle Now...

Homework Statement A sinusoidal sound wave is described by the displacement wave function s(x,t)=(2.00 μm)cos⁡[(15.7 m^(-1) )x-(858 s^(-1) )t] b) Determine the instantaneous displacement from equilibrium of the elements of air at the position x = 0.050 m at t = 3.00 ms Homework...

A very general question: What do the real and imaginary parts of a wave function correspond to physically? Cheers

Homework Statement Hello, Can you confirm that what I wrote is correct for the given potential? https://www.physicsforums.com/attachment.php?attachmentid=22309&stc=1&d=1260118852 Now I wrote the term for the wave funcation and for the given symetric potential , the functions of the...