Schrodinger's equation Definition and 108 Threads

I went through a whole calculus book and I didn't find anything that resembled sch eq. I specifically wanted to learn about that. What do you think the chapter will be called that introduced the math necessary for sch eq? Maybe it's in multivariable calculus.

Why is the rest energy usually ignored in Schrodinger’s equation? (I am aware of Dirac’s later relativistic equation.) What is the justification? Wouldn’t it change the nature of the solutions to the last equation below if it were included? Well, ok, it won't copy my Word equations. Why...

I'm getting ready to teach myself calculus with the ultimate goal of then trying to learn as much advanced physics I can in about a year's time. I've heard conflicting views about how hard this stuff is. One book said it takes two years of calculus before one can understand Schrodinger's...

Plz i want to know the practical applications of schrodinger's equation ??

The Shrödinger's equation is i \hbar \frac{\partial \Psi (\vec r, t) }{\partial t}=-\frac{\hbar ^2}{2m} \nabla ^2 \Psi (\vec r ,t ) + V(\vec r ) \Psi (\vec r ,t). Where m is the mass of the considered particle at rest. I would like to know why the pass to the relativistic equation isn't as...

Now, I have put a lot of thought into the following idea, and at different times in my life I held completely opposite views on it. It seems to me, that Schrodinger's Equation implies that the universe is deterministic, given an initial state. Now I know people will talk a lot about...

I hope this is the right place for this question. This layman has a question about Schrodigner's equation for a free particle, http://http://planetmath.org/encyclopedia/WaveFunction.html" -- just a smidge down the page, sorry I am not able to post an image of the equation -- I have a problem...

Hi there, Ok, so if you know the interactions, etc., you can calculate from time0 the probabilities for certain results at say time8. But say, however, we perform a measurement before time8. Will the original predictions for time8 still hold if a measurement is performed prior to that...

is the spectral linewidth something that is only explained by the uncertainty principle or do you also get this from schrödinger's equation? cause i would say, that schrödinger gives us discrete energy levels if we talk about atoms and therefore there should appear no linewidth. or do i need...

Hello, It's only been recently that I have acquired the math skills to deal with the time independent version of Schrodinger's Equation which is: \frac{-\hbar^2}{2m} \frac{d^2}{dx^2}\Psi(x) + U(x)\Psi(x) = E\Psi(x) I tried to derive a wavefunction that deals with a particle in a confined box...

I'm currently taking a Semiconductor class and we're talking about Schrodinger's Wave Equation, specifically the 1 dimensional time independent form. We were looking at the infinite potential well model: And we divided the graph into 3 different regions: first being the left (or...

1 - What is Wavefunction Ψ? In the derivation of the equation we treated the total energy of the electron or the particle as the kinetic energy of the particle and the potential energy 2 - Can you give an example of the potential energy of the electron?(Is it like the electric field applied...

Hi, I was looking at the relativistic equation for energy E^2=p^2+m_{0}^2 and was wondering about a methodology I took with it. Making the substitution E^2=\gamma^2 m_{0}^2 then p^2=m_{0}^2(\gamma^2-1) Considering only the \gamma-1 factor, this can be expanded...

I'm having a little trouble whit this homework assignment. Any help would be greatly appreciated. =) Homework Statement Explain if the following statements are true or false: a) Wavefunctions \phi1 and \phi2 are solutions to the time independent Schrödinger's equation, that correspond...

I've been reading some material on the Schrödinger wave equation, and quite a few sources claim that there is no derivation for the equation at all. That it essentially falls out of nowhere. This is confusing for me as I have seen some plausible derivations based on de Broglie waves. Are...

hi, i am interested in solutions to the finite-temperature schrödinger's equation for the hydrogen atom. does anybody know whether there are such? or does anybody of you know whether there is a possiblity to use something like pertubation theory to calculate the new energy-levels of the...

Hello! Here is my question: Consider a particle of mass m, whose initial state has wavefunction \psi(x), in an infinite potential box of width a. Show that the evolution under the Schrodinger equation will restore the initial state (possibly with a phase factor) after time...

Hello, I just finished learning how to solve the Schrodinger equation for the H atom and a few things trouble me. 1) The relative particle, CoM particle treatment: From what I understand, we are solving this for the case where the nucleus is taken to have mass m1+m2 and the electron has mass...

Hi, I am working on my quantum mechanics assignment and I and trying to determine the state of a system at an arbitrary time using two different methods: solving the differential equation (Schrodinger Equation) and evolution operator. I determined the final results using both methods...

So my atomic physics professor was doing a review today of quantum mechanics. One of slightly odd things he mentioned was how most of the time we solve differential quantum equation, like Schrodinger's Time Dependent Equation, using a position wave-function rather a momentum wave-function...

I've been combing over websites and papers on this, but I can't get a handle on trying to explain or visualize the similarity between them. The wave equation "smears out" over time as does the diffusion equation?

Hi Came across a guy in a cafe today who asked the question, " Why is Schrodinger's equation complex?". No one knew the answer and he didn't provide one either. What is the reason? Colin

Homework Statement Show that for a unidimensional potential of the form V(x)=v(-x), the solutions to the time independent Schrödinger's equation have a defined parity as long as these solutions does not correspond to eigenvalues not degenerated. Homework Equations -\frac{\hbar ^2}{2m} \cdot...

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...

If the electron of the h-atom is not moving in a classical orbit (like a circular orbit) why is the reduced mass used in Schrodinger's equation?

Homework Statement An electron in a one dimensional crystal is bound by: U(x) = \frac{-\overline{h}^{2}x^{2}}{mL^{2}\left(L^{2}-x^{2}\right)} for \left|x\right| < L and x = infinity for \left|x\right| \geq L Show that a stationary state for the electron in the potential well \psi(x) =...

Homework Statement Consider particles incident (in one dimension) on a potential energy step with E>U. (That is, particles of total energy E are directed along in one dimension from a region of U=0 to a region of E>U>0.) Apply the boundary conditions for \Psi and d\Psi/dx to find the...

Homework Statement Consider particles incident on a potential energy step with E<U. (That is, a particle with total energy E travels along one dimension where U=0, then crosses, at point x=0 into a region where U>E.) (The particle is incident on the potential energy step from the negative x...

I'm having some difficulty with quantum which stems from a weak math background as a shaky foundation upon which to start with an inherently difficult subject. So, if anyone would be willing to help me with some conceptual obstacles and thought exercises, I would be very grateful. These are...

Homework Statement An electron is trapped in a finite well of width 0.5 nm and depth of 50 eV. The wavefunction is symmetric about the center of the well (x = 0.25 nm). If the electron has energy 29.66 eV and ψ(0) = 1.42 (nm)-1/2, then what is the probability for finding the particle in the...

The general solution of Schrodinger's equation is givrn by -------- \Psi= A e^{kx-wt}. And this satisfies the equation . But the general solution of 3-D sinosidal wave is given by Psi= A Sin(kx-wt) And this also satisfies the schrodinger's equation. Schrodinger is credited to find the...

Hi, I'm doing a research project for my high school physics class. I originally set out to research touch screens but was disappointed with how simple the mechanics of the iphone are (or at least the basic physics of it). I continued researching and found that soon Quantum Tunneling may be...

Hi all, I was trying to explain to my girlfriend how you can `derive' Schrodinger's equation using the Planck relation E = \hbar \omega, the de Broglie relation p= \hbar k and conservation of energy. If you assume that the fundamental wavefunction is of the form \psi = e^{i(kx - \omega...

Hey everyone, I'm starting a research project for my partial differential equations course, and I've chosen to research numerical solutions to the radial form of Schrodinger's equation. From some preliminary research, I've found information on using Numerov's method, but I am really not...

I thought i had a basic to intermediate understanding of quantum physics and group theory, but when reading hamermesh's "group theory and it's application to physical problems" there's something in the introduction i don't understand. first of all, i know the parity (or space inversion)...

Homework Statement Currently I am doing a question where its asked me to show that the probability per unit length of finding a particle is independent of space and time, and is just a constant. Homework Equations The Attempt at a Solution The plane wave state I've been...

Is it true that the discrete energy level of schrodinger's equation is due to boundary condition? What is the definition of boundary condition?

i was reading up on schrodinger's equation and they had mentioned that the equation only works with 11 dimension 10 spatial 1 time. could these extra 10 spatial dimensions be harnessed and used for dimensional compression. what i mean is be able to harness the dimension and place it into an...

Many quantum physics/chemistry books use Schrodinger's equation to derive a differential equation which describes the possible wavefunctions of the system. One form of it is this: \frac{d^{2}\psi}{dx^{2}} + (\lambda - a^{2}x^{2})\psi = 0 "a" and lambda are constants. Most books solve this...

OK, I understand the physical interpretation of wave function which is the solution of Schrödinger's equation. The interpretation of wave function is in term of probability. What is physical meaning of Schrödinger's equation itself, in term of Newton's equation(F=ma)?

Hi folks! A QFT question: you start from the lagrangian, compute the hamiltonian via Legendre transform and promote the the fields to operators with canonical equal-time commutation relations. Now you can compute the relation [H,F(x)]=-\mathrm{i}\partial_0 F(x) \ , where H is the hamiltonian...

i need help coming up with a way to solve for the eigen vectors of schrodinger's time independant equation in c++. so i want to write a class that uses the shooting method, but i am not sure how to do that.

Homework Statement \frac{1}{r}\frac{d}{dr}(r^2\frac{d}{dr}\Psi (r)) + { \frac{2m}{\hbar^2}[E-V(r)] - \frac{l(l+1)}{r^2}}\Psi (r) = 0 V(r) = -Vo r\leq a 0 r > a Use \Psi (r) = \Xi (r)/r Questions asks to Find E l = 0, do I solve the general equation first or should I make l = 0 right...

Hey guys, I wanted to know if there is any other (more physical math) reason why schrodinger's equation is not valid for relativistic particles besides that it is not an invariant under lorentz.

Homework Statement Given u(x) is a solution of Schrodinger's equation: \ - \frac{\hbar^2}{2m}\frac{\partial^2\ u(x)}{\partial\ x^2 }\ + \ V(x) \ u(x) =\ E \ u(x) (i)Under what condition, u(-x) will also be a solution? (ii) If u1(x) and u2(x) be two degenerate wave functions, prove...

Homework Statement I am to show that Schrodinger's equation is linear. Homework Equations The Attempt at a Solution I think it is sufficient to show that if psi1 and psi 2 are the solutions of Schrodinger equation, then any linear combination of them, say (a psi1+b psi 2) is...

can anyone tell me the reason why they came to accept this equation with no mathematical proof behind it/ was ther any experiment that supported this equation so that it held true?

Homework Statement 1. In a region of space, a particle with zero total energy E has a wavefunction ψ (x) = A x exp - (x2/L2) a) Find the potential energy U as a function of x b) Make a sketch of U(x) versus x Homework Equations time independent schrodinger's...

I was wondering if someone could explain to me why is Schrodinger's Equation has to be linear?

why for that equation does alpha= 2E/(hf)?