Schrodinger equation Definition and 570 Threads

Hi Everybody, I am learning solid state physics using a German book called "Festkorperphysik" written by Gross and Marx. Now, in page 336 the Schrodinger equation in momentum space is introduced: \left( \frac{\hbar^2 k^2}{2m} - E \right) C_\vec{k} + \sum_\vec{G} V_\vec{G}...

Hi, I am confused about how we obtain a part of the Schrodinger equation for a particle of mass m that is constrained to move freely along a line between 0 and a. Equation: \frac{d^{2}ψ}{dx^{2}}+(\frac{8∏^{2}mE}{h^{2}})ψ(x)=0 Where does the value in the parenthesis come from and what...

We know that in Schrodinger equation, Ψ is called wave function, which is not observable, while Ψ·Ψ* is the probability, which is observable. can we rewirte the Schrodinger equation to a form without Ψ but only Ψ·Ψ*? because I think, in this way can I figure out all conservations in the...

How do I write a full Schrodinger equation, pre-approximation, for a mixture? Let's say 75% H2 and 25% He by number of particles. I already know the form and very basic applications of the Schrodinger equation and the Hamiltonian. What I want to know is, the specifics, such as how to specify...

I am reading David Griffiths' book on Quantum Mechanics, and he usually says that the general solution to the TDSE, given a potential V, can a DISCRETE linear combinations of the wavefunction solutions. However, in one section, he says that the linear discrete sum can be regarded as a continuous...

In reading Weinstock's Calculus of Variations, on pages 261 - 262 he explains how Schrodinger apparently first derived the Schrodinger equation from variational principles. Unfortunately I don't think page 262 is showing so I'll explain the gist of it: "In his initial paper" he considers...

Homework Statement I'm having a bit of trouble following my textbook, I was under the impression ψ(x) = e^i(kx) = Cos(kx) + iSin(kx) but in my textbook they write the general solution to this equation as ψ(x) = ASin(kx) + BCos(kx). How come they wrote the sin part as not imaginary? isn't this...

Homework Statement A particle of mass m is confined to move in a one-dimensional and Diract delta-function attractive potential V(x)=-\frac{\hbar^2}{m}\alpha\delta(x) where \alpha is positive. Integrate eh time-independent Schrodinger equation between -\epsilon and \epsilon. Let...

Should I start by learning about the equations for classical harmonic waves and how the de Brolier equations can be applied to them? What else should I learn? I'm a chemistry student and we did a class on quantum chemistry, but the mathematical side of it was way too complicated for me so I just...

Okay, so I'm actually an economics major but I LOVE physics; especially quantum physics. Unfortunately my knowledge of physics is limited only to the conceptual side of physics (something I'm working on changing). I spent a lot of time thinking of getting a tattoo I really wanted and settled on...

Homework Statement [2 Dimensional infinite square well] Show that you can separate variables such that the solution to the time independent schrodinger equation, ## \hat{H} \psi (x,y) = E \psi (x,y) ## can be written as a product state ## \psi (x,y) = \phi (x) \chi (y) ## where ## \phi (x)##...

There are few questions on an assignment (taken from an old exam, YIKES!) that are confounding me and I was wondering if you in the physics community could help. Here is the question; Given the wavefunction, ψ(x,t)=∫PHI(p)*exp[i((px-E(p)t)/hbar)]dp For the case where a quantum particle is...

Suppose I have a Schrodinger equation for two interacting particles located at x and y; so, something like \left( i \frac{\partial}{\partial t} + \frac{1}{2m_x} \frac{\partial^2}{\partial x^2} + \frac{1}{2m_y} \frac{\partial^2}{\partial y^2} + V(x-y) \right) \psi(x,y,t) = 0. Now, I want to...

A particle of mass m is in the state \Psi (x,t) = A e^{-a[(mx^2 / \hbar ) + it]}Find A For what potential energy function V(x) does \Psi satisfy the Schrodinger equation? Do I just re-arrange for A? (Sorry if I seem really dumb). I'm not really getting this.

Hello, this is my first thread here and i have a question regarding coherent population trapping and the dark state. I am from Germany, so please excuse me, when my english isn't very good. This is what I found on wikipedia: http://en.wikipedia.org/wiki/Dark_state in the section...

i think every system is accurately described by Schrodinger equation. so what is the point of using old quantum mechanics methods? with Schrodinger equation, at least numerically, you can solve the eigenvalues and eigenvectors readily and accurately. So what is the point of using...

How do we differentiate the solution of Schrodinger equation for closed and open system.

Homework Statement An ice-hockey puck has the weight 0.170 kg. The ice-hockey rink is 30x60 m. If no players are on the ice, what speed does the puck have due to the quantum effects (ground state)? Homework Equations The wave-equation solution to the Schrodinger equation is ψ(x,y) =...

Homework Statement The solution to the Schrodinger equation for a particular potential is psi = 0 for absolute x > a and psi = Asin(pi*x/a) for -a <= x <= a, where A and a are constants. In terms of a, what value of A is required to normalize psi? Homework Equations psi = 0 for absolute...

Homework Statement An eletron is moving along one axis between x=0 and x=L. It's mass is given by m. We want to know the energy and wave function of its possible states given by the quantic number n. Show that the solution to the above equation is En=n^2*h^2/(8*m*L^2)...

My chemistry teacher showed this slide but didn't explained how the marked step in the dedution of the schrodinger equation. Please help! I really don't know where I can find the answer, it's the first time I see the Schrodinger equation!

So I understand the schrodinger equation (independent), but I'm a kind of person who understands something better after an example or two, can someone help me and give me one for a H-atom or Hormonic Oscillator? Thanks, and sorry if this is the wrong place to put this post...

Everywhere I look,in every textbook,online texts,video tutorials,everywhere,Schrödinger equation is always solved via separating variables. I want to know is there a way to solve Schrödinger equation(of course I mean time-dependent Schrödinger equation)without separating variables? Is it...

Hi everybody! I would kindly ask you if somebody know some method to solve analitically the following equation (written in cylindrical coordinates): \Big[\frac{\partial^2}{\partial\rho^2}+ \frac{1}{\rho}\frac{\partial}{\partial\rho}+\frac{\partial^2}{\partial...

I know that one solution to the Schrodinger equation is Aexp(i(kx - ωt)) Is there a special relationship between k and ω for this to be a solution, or is it always a solution?

Should the time independent Schrödinger equation contain a differentiating 'd' as shown here: http://vergil.chemistry.gatech.edu/notes/quantrev/node8.html or a differentiating curly 'δ' as shown here: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/scheq.html Thank you!

Homework Statement What is the probability that a particle in the ground state will be found between L/2 and 2L/3? im new guys so go easy :) Homework Equations ∫ψ(x)^2 dx = ∫2/L (sin(πx/L))^2 dx in attachment The Attempt at a Solution The answer should be 30.44% i got 66.66% and sometimes a...

I'm trying to simulate wavepacket propagation in various potentials (so far in 1D). I'm writing in C++, and using allegro graphics library. The TDSE is: \frac{∂ψ}{∂t} = \frac{i \hbar}{2m} \frac{∂^2 ψ}{∂ x^2} - \frac{iV}{\hbar}ψ So what I've done was writing out the real and imaginary parts...

Homework Statement Im reading and thinking about the interpretation about Schrödinger equation s solutions (wave functions) - what they really mean. What does the amplitude of wave function correspond to? Does it mean that if amplitude is greater then energy of particle is greater as well ...

I have seen its name in many articles I have read but I would like to know. What is it and what is its use?

Does the Schrödinger equation completely neglect the uncertainty principle? If so, wouldn't this imply that our intensity distribution has its own probability distribution?

When my book deals with bound states and scattering states it puts: E<0 bound state, E>0 scattering state. What reference for the potential have been used for these?

In clssical mechanics it doesn't really seem to matter which reference point you use for your potential. All that matters is the difference in potential between two points. Does the same hold true for the potential you plug into the Schrödinger equation? It doesn't seem so since plugging in...

Hi! I think this should be a fairly easy question to resolve, but it's currently giving me fits... Suppose we consider a system of three interacting particles where we assume two of the particle (at positions r1 and r2) have infinite mass (such that we can ignore their kinetic energy) and do...

Hello, In the book physical chemistry (P. Atkins & Julio de Paula, 2009, 5 ED) the authors derive a justification of the Schrödinger equation. 1.) \frac{-\hbar^{2}}{2m} \frac{d^{2}\psi}{dx^{2}}+V(x)\psi=E \psi The derivation goes as follows: Derivation: We can justify the form of...

Classically, particles seek configurations of least potential energy. Something like this happens in QM: the wavefunction will usually be densest in those areas the potential energy is smallest. But looking at the Schrodinger equation itself, I can't see intuitively why this should be.

Homework Statement Using the Greens function technique, reduce the Schrodinger Equation for the following potential: V = V0 , 0<x<a V = infinite, elsewhere. Homework Equations The Attempt at a Solution I have no idea what "reduce" means. The professor did not go over this...

Does it have an easy classification (elliptic, hyperbolic, parabolic, for example)? Or does the fact that it has an "i" in it make this impossible?

Homework Statement An electron is confined within a three-dimentional cubic region the size of an atom where L = 200 pm. a) write a wave equation for the electron b) wirte a general wave function for the possbile states of the electorn. List any quantum numbers and their possible values...

I have learned time-independent schrodinger equation only from my textbook. I know Eψ(x) = - hbar^2 / 2m ψ''(x) + Uψ(x) and ψ(x) = Asinkx + B coskx what if it's three dimention? do I do Eψ(x, y, z) = - hbar^2 / 2m ψ''(x, y, z) + Uψ(x, y, z) ? and what is the wave equation supposed to be?

Homework Statement Consider the one dimensional wave funciton give below. a) Draw a graph of the wave function for the region defined. b) Determine the value of the normalization constant c) what is the probability of finding the particle between x = 0 and x = a/2 d) show that the wave function...

Hello guys, in the attached file, I can't understand how the guy arrived to the equation in the red rectangle. My problem is: how could there not be dC2/dt term. Why only dC1/dt term? ψ contains both C1 and C2, and when the derivative is applied, both have to be influenced, and both are...

I'm reading the Wikipedia page for the Dirac equation I am not sure how one gets a new \rho and J^\mu. How does one do to derive these two? And can anyone show me why the expression for density not positive definite?

Homework Statement When solving, say, the double delta function potential well, we fix constants using continuity. If the potential is symmetrical about the origin, can we conclude that the wave function, i.e. the solution, will also be symmetric? I found this way made the calculations much...

Hello - A few questions I have after watching Brian Green’s The Elegant Universe – Within the video Dr. Green shows a neat way to view the different scales relativity and quantum mechanics are involved with. He takes an elevator to a top floor to show relativity’s applicable scale. He steps...

Schrodinger Equation, "Potential" This is a very simple question, but I am confused. I have seen Potential and Potential Energy interchanged.. yet still referred to as potential. Is the "potential" function in the schrodinger equation really a potential function or potential energy? (units...

Hi, I several times heard that one way to describe the collapse of the wave-function is to add non linearities in the Schrodinger equation (I know that this approaches are not convincing but that's not my point), however, I don't see why a non linear SE would imply loss of unitarity? As long...

So I've been trying to understand this equation for a long time, about half a year - I don't know someone who could teach me this either due to the fact that I am only 15 and going into my final year in secondary school after August and according to most colleges (UK college, not American) in my...

While I was studying Ch 2.5 of Sakurai, I have a question about Green's function in time dependent schrodinger equation. (Specifically, page 110~111 are relevant to my question) Eq (2.5.7) and Eq (2.5.12) of Sakurai say \psi(x'',t) = \int d^3x' K(x'',t;x',t_0)\psi(x',t_0) and...

I've been looking into the time independent schrodinger equation (E\Psi = Ĥ\Psi.) I know that \Psi is the wave function and Ĥ is the hamiltonian operator. I know that Ĥ is the total of all the energies in a system. What exactly is the wave function? Is it a quantum state? And what does the E...