Schrodinger equation Definition and 549 Threads

Homework Statement An electron coming from the left encounters/is trapped the following potential: -a<x<0; V=0 0<x<a; V=V0 infinity elsewhere the electron has energy V0 a)Write out the wave function b)normalize th wave function Homework EquationsThe Attempt at a Solution for -a<x<0...

Homework Statement I was trying to solve the time-independent Schrodinger's equation for this well: http://i.imgur.com/C9QrvkX.png First I tried to look at cases where the energy of a particle is ##E < V_1##. Homework Equations Schrodinger's equation...

So I've been reading David Bohm's original paper on the alternative interpretation of quantum mechanics in terms of hidden variables, just out of interest. In the 4th section he presents a complex function ψ in terms of R and S, and then (using the time dependent schrodinger equation, TISE)...

The Nonlinear Schrodinger Equation (NSE) is presented as: $$i\frac{∂A}{∂z} = \frac{1}{2}β_2\frac{∂^2A}{∂t^2}-\gamma|A^2|A$$ The steady state solution $$A(z)$$ Can be derived as an Ansatz given by: $$ A(z) = \rho(z)e^{i\phi(z)}$$ By substituting and solving the ODE, the steady state...

I am self studying the Book- Introduction to Quantum Mechanics , 2e. Griffith. Page 47. While the book has given a proof for eq. 2.64 but its not very ellaborate Integral(infinity,-infinity) [f*(a±g(x)).dx] = Integral(infinity,-infinity) [(a±f)* g(x).dx] . It would be great help if somebody...

okay so i need some help interpreting some of the results, so (-ħ2/2m)Ψ''=E-V0Ψ; So i set k2= 2m*(E-V0)/ħ2 and so : Ψ''=-k2Ψ so if V0=0 or is smaller than E, k2 is positive; *need for help starts here* Ψ=Aeikx+Be-ikx; another result for this would also be only eikx so is the second term only...

Homework Statement Homework EquationsThe Attempt at a Solution It is a short question so I don't suppose it is difficult. However, I don't really understand what it is asking for : 1.The TDSE itself is already a 2nd-order differential equation (if you substitute the terms back into H). 2...

Can someone please explain what's going on at 47:40 Thanks in advance.

The question I have is regarding the time-variant form of schrodinger's equation. Can I just put a complex number of form c=a+bi where the i is in it or can I just literally put sqrt(-1) where the i is: addendum: sorry forgot the t in the right-hand term, it should read (r,t) instead of (r)...

Homework Statement [/B] Q18. Which of the following statements about Schrodinger equation is true? A) The exact solution of the equation never exists B) It is only applicable to the hydrogen-like atoms C) We can know the energy of the atomic orbital by solving the equation D) The square of the...

Homework Statement Two identical particles, each of mass m, move in one dimension in the potential $$V = \frac{1}{2}A(x_1^2+x_2^2)+ \frac{1}{2}B(x_1-x_2)^2$$ where A and B are positive constants and ##x_1## and ##x_2## denote the positions of the particles. a) Show that the Schrodinger equation...

Hi, I am wondering why every general solution to Schrodinger equation can be built from separable solutions. In other words, I don't follow that why every solution to Schrodinger equation can be written as $$\Psi(x,t) = \sum c_n\Psi_n(x,t)=\sum c_n\psi_n(x)\phi_n(t)$$ I know that the right hand...

Hi All, What are the main differences between statistical and dynamics properties in physics? Could you please explain the difference for problems in both classical and quantum mechanics. For instance, path integral molecular dynamics is supposed to give statistical properties of a quantum...

The problem looks very simple. We have a time-dependent Hamiltonian: $$H(t) = B(t)H_0$$, where ##B(t)## is a numerical function, and matrix ##H_0## is time-indpendent. Let us consider: $$B(t) = \begin{cases} 1,&\text{for $0\leq t\leq t_0$}\\ A,&\text{for $t>t_0$.} \end{cases}$$ Also, let us...

Suppose I want to solve the Schrödinger equation numerically for some potential V(x). The easiest way to do so, is to discretize it on a grid of finite length, and apply a finite difference scheme to approximate the second order derivative. Doing so yields an eigenvalue equation on matrix form...

Hi, Can anyone please explain the physical meaning of coherence(Quantum Mechanics). Thanks is advance

Homework Statement This is a (long) multi-part question working through the various stages of solving the radial Schrodinger equation and as such it would be impractical to type it all out here but I will upload the pdf (https://drive.google.com/open?id=0BwiADXXgAYUHOTNrZm16NHlibUU) of the...

Homework Statement Let us look at a 3-dimensional potential box. Show, that the wave function in this situation can be written as the product of 3 single-argument functions. Homework Equations The 3D Schrödinger equation: \begin{equation} -\frac{\hbar^2}{2m} \left( \frac{\partial^2...

When we are measuring the spin of the electron in the experiment, we choose the spin property as its eigen state for the measurement. The eigen vectors corresponding to these states could be time dependent. Can we still break the problem into solving time independent Schrodinger Equation and...

Homework Statement In a potential box (##L = 1.00pm##) an electron moves at a relativistic speed, meaning it's momentum can't be expressed as ##P = \sqrt{2mE}##. a) Using the uncertainty principle, show that the speed is indeed relativistic b) Derive an expression for the allowed energy states...

In the (b),I have some questions: (1) Does it mean ψ can be real or not real? (2) Why do the solutions of linear combination must have the same energy? As I know, these solutions are often different, as long as they are eigenvalues of time-independent Schrodinger equation. (3) In the sentence...

The normalized angular wave functions are called spherical harmonics: $$Y^m_l(\theta,\phi)=\epsilon\sqrt{\frac{(2l+1)}{4\pi}\frac{(l-|m|)!}{(l+|m|)!}}e^{im\phi}*P^m_l(cos\theta)$$ How do I obtain this from this(http://www.physics.udel.edu/~msafrono/424-2011/Lecture 17.pdf) (Page 8)? The...

Hello I am little bit confused about one topic on theoretical Physics and that is If we want to describe our Quantum world (example atoms in metal) then should I use Quantum field theory or Quantum mechanics?

Suppose I want to solve the time-independent Schrödinger equation (ħ2/2m ∂2/∂x2 + V)ψ = Eψ using a numerical approach. I then discretize the equation on a lattice of N points such that x=(x1,x2,...,xN) etc. Finally I approximate the second order derivative with the well known central difference...

Schrodinger Equation is the very first step when we start learning QM. However, I never learned about the physical meaning of it. I have read a number of articles and discussion online. Regarding the ones I understand, there are generally two points of view. 1. Fundamental physical laws are not...

Homework Statement Alrighty, so here's my problem in a nutshell: Some particle of mass m is confined to move along a ring of radius R. Since it's on a ring, it has periodic boundary conditions--i.e.: For the boundary defined as ##-\pi R \leq x \leq \pi R##, ## x = -\pi R ## and ## x = \pi R...

Homework Statement Normalized equation for particle in a ring, where V=0 on a ring of radius 'a' and infinite everywhere else. Homework EquationsThe Attempt at a Solution Replcing x by rθ, $$-\frac{\hbar^2}{2I}\frac{\partial^2\psi}{\partial\theta^2}=E\psi$$ By guess, I found out that...

So I have previously learned how to discretize the Schrödinger equation on the form: (p^2/2m + V)ψ = Eψ , where the second order derivative is approximated as: (ψi+1+ψi-1-2ψi)/2Δx Such that the whole equation can be translated into a matrix eigenvalue-equation. The problem is that I am now...

Hi, I am a student in the Netherlands, currently 17 years old and at the end of my 'middelbare school', meaning that next year I'll be a bachelor student at a university. I am doing an extended essay/research thing that is custom you do in your last year, with a friend of mine. We picked the...

Hi folks, I just want to check I understand correctly the Schrodinger equation for two electrons. https://en.wikipedia.org/wiki/Schrödinger_equation#Time-independent_equation With control F you can find "two electrons atoms or ions" section. Let's assume the wave function = x1 2+ x22 and...

Homework Statement Lets say f(x) is a solution to TISE. If it is, why is its complex conjugate f*(x) a solution too? Homework Equations TISE = time independent Schrodinger equation The Attempt at a Solution ?

Hi. I'm wondering how different potentials, such as the Dirac-Delta potential, linear potential, quandratic potenial, etc., are implemented experimentally. I only understand how the Schrodinger equation is solved if these are the potentials and I'd like to have a better understanding of quantum...

The Dirac equation is the more generalized form of the Schrodinger equation and accounts for relativistic effects of particle motion (say an electron) by using a second order derivative for the energy operator. If you have an electron that is moving slowly relative to the speed of light, then...

Why doesn't The Feynman Lectures consider the possibility of negative ##\alpha## when it says that ##e^{+2\alpha\rho}## is a rapidly increasing exponential (just below http://feynmanlectures.caltech.edu/III_19.html#mjx-eqn-EqIII1923) ?

I know there's a similar post, but i didn't understand it. Why the derivative respect to t in terms of the complex conjugate of ψ is: instead of being the original S.E in terms of ψ* or the equation in terms of ψ with the signs swapped

I'm trying to numerically solve the time dependent Schrödinger equation and I've been told that the best approach is to numerically integrate using a finite difference method, however I don't understand why I couldn't just use ode45 to solve it?! Is the finite difference (interpolation) method...

Given 1A.1 and 1A.2, I have been trying to apply the Schrödinger equation to reproduce 1A.3 and 1A.4 but have been struggling a bit. I was under the assumption that by applying ##\hat{W} \rvert {\psi} \rangle= i\hbar \frac {d}{dt} \rvert{\psi} \rangle## and then taking ##\langle{k'} \lvert...

Hello everyone, I have this weirdo potential for homework \begin{equation} U(x) = \frac{U_1}{ \left( 1+e^{x/a}\right)^2 } - \frac{U_2}{ \left( 1+e^{x/a}\right)} \end{equation} where U1,U2 and "a" are positive and I need to find the energies for the bound states and also the wave functions...

Hi everyone, I am trying to find electron wavefunction of a system I am working in. Numerical method I choose is the Variational method (VM). This method is convenient to find the ground state of the system. More details are available here. Problem I have can be explained on a very simple...

So I'm trying to figure out how we got the allowed vibrational energy levels for a diatomic molecule by approximating it with simple harmonic motion. I do know how to use the uncertainty principle to get the zero-point energy: We know that the potential function is ##V(x) = \frac{1}{2}mx^2##...

Homework Statement I have an attachment Homework Equations Schrödinger equation The Attempt at a Solution The issues I am having is how to start this one. This is not a infinite square well but a semi-infinite square well. I know that energy= K^2= 2mE/h^2 Where h is planks constant 6.626 X...

Homework Statement Problem: Consider a "crystal" consisting of two nuclei and two electrons arranged like this: q1 q2 q1 q2 with a distance d betweem each. (q1=e, q2=-e) a) Find the potential energy as a function of d. b) Assuming the electrons to be restricted to a one-dimensional...

I'm trying to integrate the Schrodinger equation ##i\hbar \frac{d}{dt} |\psi(t)\rangle = H |\psi(t)\rangle## with the initial condition ##|\psi(t_{0})\rangle=|\psi_{0}\rangle## to show that ##|\psi(t)\rangle = \exp(\frac{t-t_{0}}{i\hbar}H)|\psi_{0}\rangle##. I know how to plug in the solution...

According to my textbook the nonlinear Schrödinger equation: $$\frac{\partial A(z,T)}{\partial z} = -i \frac{\beta_2}{2} \frac{\partial^2A}{\partial T^2} + i \gamma |A|^2 A \ \ (1)$$ can be cast in the form $$\frac{\partial U(z,\tau)}{\partial z} = -i \frac{sign \beta_2}{2} \frac{1}{L_D}...

If we were to assume that the electron moves around the proton with radius a, the Schrodinger equation becomes: ##\frac{1}{a^2}\frac{d^2\psi}{d\phi^2} + \frac{2m}{\hbar^2}|E|\psi = 0## The question in my textbook asks me to solve the above equation to obtain values of energy and angular...

Suppose we have an electron in a hydrogen atom that satisfies the time-independent Schrodinger equation: $$-\frac{\hbar ^{2}}{2m}\nabla ^{2}\psi - \frac{e^{2}}{4\pi \epsilon_{0}r}\psi = E\psi$$ How can it be that the Hamiltonian is spherically-symmetric when the energy eigenstate isn't? I was...

Homework Statement Trying to use change of variables to simplify the schrodinger equation. I'm clearly going wrong somewhere, but can't see where. Homework Equations [/B] Radial Schrodinger: -((hbar)2)/2M * [(1/r)(rψ)'' - l(l+1)/(r^2) ψ] - α(hbar)c/r ψ = Eψ The Attempt at a SolutionWe're...

Is the solution of the time-independent schrodinger equation always a stationary state? Can it be non-stationary?

Hi, in the book 'Introduction to Quantum Mechanics' by Griffiths, on page 71 in the section 'The Delta-Function Potential' he states that the general solution to time independent Schrodinger Equation is $$\psi(x) = Ae^{-\kappa x} + B e^{\kappa x}$$ he then notes that the first term blows up as...

Just like it says, are all solutions of the 1D time independent Schrodinger equation, by default, energy eigenstates? I'm having a hard time imagining how solutions, with these conditions, that aren't energy eigenstates could exist if they have to satisfy the relation E \psi(x)=\hat{H}\psi(x)