Mathematica Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us, Your solution approach seems overly complicated because it still requires matching the derivatives at $RM$ after already having introduced the (not strictly valid) condition of vanishing amplitude at $10RM$. In quantum physics, you may need to simplify and split the Schrödinger equation for hydrogen. Numerically solving a simple Schrodinger equation with fast Fourier transforms. I am confused about solving Schrodinger equation numerically. Example Suppose we want to verify the energy of the ground state wave function of the hydrogen atom, and . Could you please also add to your answer how we can solve the time-independent Schrodinger equation? Schrödinger sure deserved the Nobel Prize ! Want to improve this question? MathJax reference. (2) To solve Schrödinger wave equation for hydrogen atom and analyze its specific solutions. Solve the angular part of Schrodinger equation numerically. Was the theory of special relativity sparked by a dream about cows being electrocuted? Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. So I can set the wave function at (r=0) to any arbitrary value, say 2 and then I have the other condition on the derivative. Forecasting Prices vs Returns by Deep Learning. As Sitaram Bettadpur correctly answered, this is a standard problem in Quantum Mechanics. This wavefunction is the stationary state, and the scaling factor is the energy. I'm trying to solve Schrödinger 1D equation for hydrogen atom but I found several difficulties. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Why are the divisions of the Bible called "verses"? Is Elastigirl's body shape her natural shape, or did she choose it? To simplify the usual Schrödinger equation, you switch to center-of-mass coordinates. Podcast 289: React, jQuery, Vue: what’s your favorite flavor of vanilla JS? At this point, we can write down the Schrodinger equation $H\psi=i\hbar\frac{\partial \psi}{\partial t}$: $$\frac{-\hbar^2}{2m}\nabla^2\psi - \frac{e^2}{4\pi\epsilon_0 r}\psi=i\hbar\frac{\partial \psi}{\partial t}$$. How to change the default normalization for NDEigensystem? What modern innovations have been/are being made for the piano. In position space, the equation is now, for a time-independent wavefunction $\psi(\vec{r})$, $$\frac{-\hbar^2}{2m}\nabla^2\psi - \frac{e^2}{4\pi\epsilon_0 r}\psi=E\psi$$. Deploying Profiles and Fields with SFDX in VSCode. Why does the Schrödinger equation work so well for the hydrogen atom despite the relativistic boundary at the nucleus? I'm not very familiar with coding in Mathematica but I'd like to plot the solutions (actually Spherical Harmonic orbital solutions) of the Schrödinger equation for the hydrogen atom. Why is a link in an email more dangerous than a link from a web search? From the analytical solution for the hydrogen atom I remember that the energies were obtained by boundary conditions and then the energy depends on n*n in which n is interpreted as different energy levels. Is there a formal name for a "wrong question"? The Hamiltonian will contain a kinetic-energy term for the electron and a Coulomb potential term: $$H=\frac{\hat{\vec{p}}^2}{2m}-\frac{e^2}{4\pi\epsilon_0 \hat{r}}$$. Should we leave technical astronomy questions to Astronomy SE? To learn more, see our tips on writing great answers. I tried on this way because using one, Schrödinger equation for Hydrogen atom [closed]. Schrodinger wave equation describes the behaviour of a particle in a field of force or the change of a physical quantity over time.