Schrodinger equation Definition and 569 Threads

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

All copyright reserved to Prof. Harbola and NPTEL, Govt. of India. Duplication punishable offence. Course Website: http://www.nptel.ac.in/courses/115104096/

Homework Statement Assume that Planck's constant is not actually constant, but is a slowly varying function of time, $$\hbar \rightarrow \hbar (t)$$ with $$\hbar (t) = \hbar_0 e^{- \lambda t}$$ Where ##\hbar_0## is the value of ##\hbar## at ##t = 0##. Consider the Hydrogen atom in this case...

Hello all, you may already know that Q.M. is a linear theory however there is something called nonlinear Sch. eq. for example Gross-Pitaevskii equation. How can such a thing exist considering that Q.M. is a strictly linear theory. Cheers.

When reading a textbook I came across some reasoning about Schrödinger Equation. It started with the wave function $$\nabla^2\psi=k^2\psi$$ I am a bit lost at this point. Where does the right side of the equation come from? What should I review to fix that part of my knowledge?

I recently found this article about the dynamics of the wave function. It has some good simple illustrations and I found it valuable. But the author has a question himself, about understanding the Schrodinger equation. I wonder if anybody here could fill in the missing piece. The relevant part...

The time-dependent Schrodinger equation is given by: ##-\frac{\hslash^{2}}{2m}\triangledown^{2}\psi+V\psi=i\hslash\frac{\partial }{\partial t}\psi## Obviously, there is a laplacian in the kinetic energy operator. So, I was wondering if the equation was rearranged as...

This is a basic question, so probably easy to answer. The following from Wikipedia seems pretty standard while describing the Schrödinger equation: "...and Ĥ is the Hamiltonian operator (which characterises the total energy of the system under consideration)." On the other hand, from page 100 of...

Homework Statement I am being asked to show that the wave function ψ and dψ/dx are continuous at every point of discontinuity for a step potential. I am asked to make use of the Heaviside step function in my proof, and to prove this explicitly and in detail. Homework Equations...

I am trying to see how I can use the schrodinger equation to quantify the changes in the intensity of light. My closest guess is using the time dependent pertubation theory

Hi at all, I'm tring to solve Schrodinger equation in spherically symmetry with these bondary conditions: ##\lim_{r \rightarrow 0} u(r)\ltimes r^{l+1}## ##\lim_{r \rightarrow 0} u'(r)\ltimes (l+1)r^{l}## For eigenvalues, the text I'm following says that I have to consider that the...

Hi, I have been looking in various text about how to find an admissible solution to the Schrödinger eqn in one dim. in the harmonic oscillator model. As in MQM, the solutions to this are said to be ##Ae^{ikx}+Be^{-ikx}##, which are then said to be not admissible. The book then goes straigtht to...

I am interested in Schrodinger equation with the temporal element and the calculation of the probability when its depend on 3 variable coordinate and time? How to calculate it and norm it? Probability = (integral x,y,z...0 to infinity) * (integral t...0 to infinity)=1 ?

Hi everybody! I need to compute a C++ program for solve Schrodinger equation and calculate nuclear density. My nucleus is made up of only neutrons immersed in a potential of a harmonic oscillator. Schrodinger equation is: $$[-\frac{\hbar^2}{2m}\triangledown^2+V_{HO}(r)]\psi=E\psi$$ with...

Hi, in QM literature the inadmissible solutions to the Schrödinger eqn are often , if not always, quoted in the text as "inadmissible", because they are discontinuous, not-single valued, not square integrable and not infinitely differentiable. However in a discussion with Dr Du yesterday...

I have reviewed the various posts on gauge symmetry in particular this one which is now closed. In this post there is the following link:http://www.vttoth.com/CMS/physics-notes/124-the-principle-of-gauge-invariance. This is a good read. However, there is some clarification I need. The...

Hi guys! For nuclear case, I need to write an Schrodinger equation in cylindrical coordinates with an total potential formed by Woods-Saxon potential, spin-orbit potential and the Coulomb potential. Schrodinger equation can be written in this form: $$[-\frac{\hbar^2}{2m}(\frac{\partial...

Hi, I noticed that the raising and lowering operators:\begin{equation} A =\frac{1}{\sqrt{2}}\big(y+\frac{d}{dy}\big) \end{equation}\begin{equation} A^{\dagger}=\frac{1}{\sqrt{2}}\big(y-\frac{d}{dy}\big) \end{equation}can be used to solve the eqn HY = EY However I am curious about something...

Dear all, sorry I made a new post similar to the previous post "Initial conditions..", however, a critical point was missed in the previous discussion: The initial conditions y(0)=1 and y'(0)=0 are fine and help in solving the Schrödinger equation, however, studying free electrons, the equation...

Hi, I am wondering if there exists some general initial conditions for solving the Schödinger eqn. for 1D free electrons ? Thanks!