Schrodinger equation Definition and 569 Threads

I've tried to solve Schrodinger equation for Charmonium and Bottomonium and there are some problems with that : 1. As we know the Schrodinger equation is independent from quantum number "ml" so there would be same Energy for different "ml" for a specific n. But what we see in PDG book is...

Why is the TDSE first derivative in time. Now I know that it is required so that the wave functions are complex... but is there any physical interpretation for this requirment??

Hi there, during my work on my PhD thesis as an experimental physicist I ended up with a very theoretical problem: What does the wavefunction of an electron traveling through a magnetic vector potential look like? I chose a cylindrical coordinate system with a magnetic vector potential A...

Schrodinger Equation in momentum space? ?? I don't know if this makes any sense at all, but I'm studying QM and just trying to generalize some things I'm learning. Please let me know where I go wrong.. Basically by my understanding the most general form of the Schrodinger Equation can be...

In standard, run-of-the-mill, one-dimensional scattering problems (e.g., finite square wells), we calculate transmission and reflection amplitudes by (in part) making sure that our wave function \psi satisfies the following conditions at discontinuities of the potential: (1) It is continuous...

I tried simply substituting z and epsilon into the original equation. I managed to get the second term of the left hand side correct but not the first term as I don't know how to turn z into d^2/dz^2. Can you please give me suggestions as to how I can approach this question. Thanks

From what I see, the time dependence in potentials do not change the spatial aspect of the wave function. They contribute a time dependence to the population of what were originally stationary states. If this is the case, then does that imply that the time independent bases are the ones we...

Homework Statement a particle of mass m moving in one dimension has potential energy V(x)=0.5m [[omega(subscript0)]^2] x^2 verify that psi0 (proportional to) exp [(-m omega0 x^2)/2 h bar] and psi1 (proportional to) exp [(-m omega0 x^2)/2 h bar] are both solutions of the time...

hi, can anybody of you show me how the schrödinger equation with the spin term of the electron for the hydrogen atom looks like? i really do not know how to do this Gavroy

Homework Statement Given a set of solutions |psi_n> to the TISE show that a) |Capital-psi>=Sum(C_n|psi_n>) is not a solution to the TISE Homework Equations ***H|psi_n>=E_n|psi_n> The Attempt at a Solution I don't really know where to start, I plugged |psi_n> into *** and I am...

Pardon my ignorance but why does the Time Independent Schrödinger equation use Time? It uses a kinetic energy operator. Kinetic energy; "It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity." Velocity is; "The scalar absolute value...

This extract is from my college notes. "Because of the inherent difficulty of obtaining even grossly approximate solutions of the complete Schrodinger equation, one typically focuses on reduced formulations that are believed to capture the essential features of the problem of interest. This...

Homework Statement Show that, if psi1 and psi2 are both solutions of the time-dependent Schr¨odinger equation, so is c(subscipt1) psi1 + c(subscript2) psi2 (where c1 and c2 are arbitrary constants). Homework Equations The Attempt at a Solution every source I've consulted so far...

in the schrodinger equation the integration constant in the angular wave equation is set to L(L+1). may i know why this is set ,what is the reason , thx!

Prove this function satisfies the time independent schrodinger equation. When V is constant. Psi = A e^(i k x) + B e^(-i k x) Attempt: Time independent schrodinger equation : (- (hbar^2) / 2m) * (d^2 Psi / d x^2) + V Psi = E Psi Second order derivative of Psi : (-k^2 A e^(i k x)) + (-...

Homework Statement Use the ground-state wave function of the simple harmonic oscillator to find xav, (x2)av, and \Delta x. Use the normalization constant A=(\frac{m\omega _0}{\overline{h} \pi })^{1/4}Homework Equations \psi (x) = Asin(kx) (f(x))_{av} = \int ^{\infty }_{-\infty } \left| \psi (x)...

Homework Statement I have a 2D square well with sides a. What is the minimum momentum and energy for this well? Homework Equations Minimum momentum given by Δp≈ℏΔx and Δp≈ℏΔy Minimum energy given by ΔE≈ℏΔt This might be right. It says to consider the Schrödinger Equation in 2D. I've never...

I have been studying QM and am interested in keeping to the non-relativistic theory for now. In many experiments of crossed gamma rays in the vicinity of a massive particle (or nucleus), pair generation of an electron and its anti-particle the positron is well described. In some instances, the...

Homework Statement see attachment Homework Equations TISEThe Attempt at a Solution a)When U>E -\frac{\hbar^2}{2m}\frac{d^2\Psi(x,t)}{d x^2}+U(x)\Psi(x)=E\Psi(x) leads to blahblahblah...(there is only transmittion no reflection as x to infty) \Psi(x)=Be^{-\alpha x}, where \alpha =...

Hi, I am having trouble understanding an example from a textbook I am reading on the Schrodinger equation. The example deals with an infinite square well in one dimension. With the following properties: V = 0\,where -a \leq x \leq a V = \infty\,|x| \geq a Where V is the potential. The...

How can time-independent schrödinger equation be proven? Do you know any source which explains it clearly? Thanks for replies.

Hi everyone, How can I solve hydrogen atom with discrete nonlinear schrödinger equation? Could you help me with the mathematics of that, please?

i know its a stupid question but I am a beginner: according to eisntein: E=K+m_{o}c^2 but the plane wave solution yields that particle's KE is its total energy,where free particle has no potential energy. But where is the rest mass energym_{o}c^2? Is it omitted?

1. I am writing one page on if there is free will(using physics). I concluded that there is no free will and I am trying to use Schrödinger equation in my paper, but i don't understand what its proving/means. And if possible can i get an example that will prove the equation(no math, just an...

Im new to all of this a just started studying quantum mechanics and the time-dependent schrodinger equation. What attributes must be known of a particle to use the schrodinger equation? Also is the wave function considered a constant?

Forgive me if this is a poorly asked question but I am not yet completely fluent in quantum mechanics and was just looking at the energy eigenvalue equation H|\Psi\rangle = i\hbar \frac{\partial}{\partial t}|\Psi\rangle = E|\Psi\rangle . We've got the Hamiltonian operator H acting on the state...

Hi every one .. Could anyone provide me a link of original schrodinger equation article in english?? I'll really approciate that

Homework Statement Write down the time independant schrodinger equation in the momentum representation for a particle with mass m when the potential is given by V (x) = 1/2 \gamma x2. A possible soloution of this schrodinger equation is of the form \Psi (p) = Ae-Bp2 / 2 Determine...

Hi there, I was expecting to find a "simulations forums" somewhere here, if there is a better place for this thread please let me know :) OK, here's the problem: I'm trying to make a simulation with PYthon, at first with a square potential, for simpler potential/boundary conditions. But...

What does it mean to "satisfy" the Schrodinger equation? Homework Statement Show that the 2p wave functions of the hydrogen atom satisfy the radial Schrodinger eq. One of the radial equations for the 2p state is \frac{1}{\sqrt{96 \pi a^{3}}} \frac{r}{a} e^{\frac{-r}{2a}} Homework Equations...

Homework Statement Starting with \psi(r,\theta,\phi)=R(r)Y(\theta,\phi) saubstitute into the Schrodinger equation and show (using the technique of separation of variables) that R satisfies: (\frac{\hbar^2}{2m}\frac{1}{r^2}\frac{d}{dr}(r^2\frac{d}{dr})+\frac{C}{2mr^2}+V(r))R=ER(r) Homework...

Homework Statement Hi, I've just started this new course about quantum mechanics and it begins, among others, with this question: [PLAIN]http://img710.imageshack.us/img710/2962/unbenanntfwg.jpg I'm really at a loss how to approach this one. Can anyone please help?

Homework Statement A particle of mass m and total energy E < 0 is confined to a potential given by: where \alpha is some positive constant. Show that the wavefunction is a solution of the time independent Schrodinger equation when x > 0. Find the associated energy Eigenvalue E.Homework...

Why does charge of a particle not appear in Schrodinger Equation even though mass appears? Chapter 5 Q No. 9 Quantum Physics of Atoms Molecules Solids Nuclei and Particles - Robert Resnick, Robert Eisberg

Homework Statement Consider reflection from a step potential of height V0 with E > V0, but now with an infinitely high wall added at a distance a from the step (x=0 at V=V0) Solve the Schrodinger equation to find \varphi(x) for x<0 and 0 \leq x \leq a. Your soultion should contain only one...

Can someone help me with this problem? show that the angular wavefunction Y1,1 is a solution to the schrodinger equation.

Some books begin QM by postulating the Schrodinger equation, and arrive at the rest. Some books begin QM by postulating the commutator relations, and arrive at the rest. Which do you feel is more valid? Or are both equally valid? Is one more physical/mathematical than the other? I...

The Pauli equation (seen here) contains its spin dependence in the term which reads \frac{1}{2m}\left[ \sigma\cdot\left(p-\frac{e}{c}A\right)\right]^2 So let B be any vector. Then \left( \sigma\cdot B\right)^2 =\left(\sigma_1 B_1 +\sigma_2 B_2 + \sigma_3 B_3\right)\left(\sigma_1 B_1...

Homework Statement I've attached my past paper question, which contains the relevant integral identity too. The Attempt at a Solution This question is relatively simple, yet I can't seem to complete it. I used the schrodinger equation which is: -(ħ²/2m)\nabla^2u + Vu = Eu...

Homework Statement This is really a maths problem I'm having. I need to get the general solution for the infinite square well in the form: u = A cos(kx) + B sin(kx) I found the general solution to be: u = A exp(ikx) + B exp(-ikx) Using Euler's formula: exp(ikx) =...

I am sure you are all aware of the Schrodinger equation. The Hamiltonian is included in this equations, which contains the Kinetic energy operator. When Schrodinger wrote thi he converted momentum to the unit imaginary number, the reduced Planck constant and the Delta operator. My...

Homework Statement In delta potential barrier problem Schrodinger equation we get \psi(x)=Ae^{kx}, x<0 \psi(x)=Ae^{-kx}, x>0 We must get solution of lim_{\epsilon \rightarrow 0} \int^{\epsilon}_{-\epsilon}\frac{d^2\psi}{dx^2}dx Homework Equations The Attempt at a Solution lim_{\epsilon...

ive been asked to show that the function of Y(x) = A sin (x) = 0 is a solution to the equation of d2Y(x) dx2 +k2Y(x)=0 where the Y is meant to be the lowercase wavefunctio psi...i just can't get it to work on this :( basiaclly I am completely...

Homework Statement Homework Equations This is what I'm trying to obtain, in terms of the elements in the question. Assuming that these 'x' values are 'z'. The Attempt at a Solution I'm not really understanding what it is being asked here. Do I just substitute the value of V(z) into...

While messing around with the Schrödinger equation on paper, I found an interesting, elegant way of expressing it. Let P be the probability density |\Psi |^2, and let \vec Q be a real-valued vector field. \vec F is a vector field describing the forces acting on the system when in a given...

In his lectures on Quantum Physics, Richard Feynman derives the Hamiltonian matrix as an instantaneous amplitude transition matrix for the operator that does nothing except wait a little while for time to pass.(Chapter 8 book3) The instantaneous rate of change of the amplitude that the wave...

I just have a small question, In my book it says that the schrodinger equation, i\hbar\frac{\partial\Psi}{\partial t} = \frac{\hbar^2}{2m}\frac{\partial^2\Psi}{\partial x^2} + V\Psi rearranged is, \frac{\partial\Psi}{\partial t} = \frac{i\hbar}{2m}\frac{\partial\Psi ^2...

I can understand that if z= a + ib then z*=a - ib, where the definition of the complex conjugate is reversing the sign in front of the imaginary part. I'm now confused about how the complex conjugate works in the TISE. in a stationary state, i\hbar\frac{\partial\Psi}{\partial\\t}= E\Psi...

Homework Statement Show that the time-dependent Schrodinger equation is separable when V depends on time only and is uniform in space (i.e., V = V (t)). Homework Equations The Attempt at a Solution In the attached document

hey guys first post so sorry if this has already been asked :S what exactly is meant by the separation of variables in the schrodinger equation? also what co-ordinate system would i use to solve for an electron in a hydrogen-like ion? thanks