Schrödinger Definition and 611 Threads

Erwin Rudolf Josef Alexander Schrödinger (UK: , US: ; German: [ˈɛɐ̯viːn ˈʃʁøːdɪŋɐ]; 12 August 1887 – 4 January 1961), sometimes written as Erwin Schrodinger or Erwin Schroedinger ("oe" is the proper transliteration of the German "ö"), was a Nobel Prize-winning Austrian-Irish physicist who developed a number of fundamental results in quantum theory: the Schrödinger equation provides a way to calculate the wave function of a system and how it changes dynamically in time.
In addition, he was the author of many works on various aspects of physics: statistical mechanics and thermodynamics, physics of dielectrics, colour theory, electrodynamics, general relativity, and cosmology, and he made several attempts to construct a unified field theory. In his book What Is Life? Schrödinger addressed the problems of genetics, looking at the phenomenon of life from the point of view of physics. He paid great attention to the philosophical aspects of science, ancient and oriental philosophical concepts, ethics, and religion. He also wrote on philosophy and theoretical biology. He is also known for his "Schrödinger's cat" thought experiment.

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  1. A

    Numerical solution of Schrodinger equation script

    I am right now working on a script that solves the Schrodinger equation numerically for arbitrary potentials using the finite difference method. The idea is that I diagonalize the Hamiltonian with elements: H(i,i+1)=1/dx^2 * constants H(i,i-1)=1/dx^2 * constants H(i,i) = -2/dx^2 * constants and...
  2. A

    Schrodinger equation numerical solution

    I have written a program that solves the Schrödinger equation numerically using the finite difference method based on the attached article. The end goal is to make a program that solves the Schrödinger and Poisson equations self-consistently for the conduction band in different heterostructures...
  3. M

    Schrodinger equation - stationary states

    two questions: 1. besides using Ehrenfests theorem, is there another way of showing that the expectation value of momentum is zero in a stationary state ? (I don't see it when simply applying the definition on the stationary solution) 2. If we have a state that is a superposition of...
  4. L

    What is the condition for a particle to go into a square potential well?

    Hello everyone I am searching for the answer for the condition (related to the total energy of the particle E) for which any particle will go into the square potential well. I have studied Griffiths's quantum mechanics book Introduction to the quantum mechanics Section 2.5 and 2.6) but still...
  5. quantumfunction

    I Schrodinger's cat, the multiverse and isolated systems

    I know the debate about Schrodinger's cat is usually about things like consciousness but I want to talk about what it might say about isolated systems. Does the wave function of isolated systems remain in a superposition of observable states no matter how large the system gets? Say you have...
  6. D

    Scaling when solving Schrodinger equation numerically

    I guess this is just a maths problem about algebra. I'm learning to solve Schrodinger equation numerically, and right now I'm just dealing with the simplest examples like harmonic potential, square well, etc. The problem is that sometimes my program gives some strange results and I suspect it is...
  7. olgerm

    Schrödinger equation for 2 particles

    U(x,y,z,t)*ψ(x,y,z,t)-(ħ/(2*m))*(d2ψ(x,y,z,t)/dx2+d2ψ(x,y,z,t)/dy2+d2ψ(x,y,z,t)/dz2)=ħ*i*dψ(x,y,z,t)/dt qproton=-qe Schrödinger equation for electron in hydrogen atom (if we consider proton as point charge which is moving at a constant speed vproton→=(vp;x;vp;y;vp;z).) is...
  8. P

    Derivation of Time Dependent Schrodinger Equation

    Hi All, I have problem in understanding one step in the derivation of the time dependent Schrodinger Equation. Please see attached file page 2 (marked in red). Most grateful if someone can help! Peter Yu (This is from Quantum Mechanics The Theoretical Minimum Page 99-102)
  9. Dyatlov

    General solution for the time-dependent Schrödinger equation

    Hello! I have two uncertainties (hehe) about two concepts from a QM time-dependent Schrödinger equation video. The video is I cannot move on further if I don't fully grasp everything he explains in the video. My two issues are: 1) The general solution for the time-dependent Schrödinger...
  10. S

    Boundary conditions of the radial Schrodinger equation

    Consider the radial differential equation ##\bigg( - \frac{d^2}{dr^2} + \frac{(l+\frac{d-3}{2})(l+\frac{d-1}{2})}{r^2} + V(r) + m^2 \bigg) \phi_l (r) = \lambda\ \phi_l (r)##, which I've obtained by solving the Schrodinger equation in ##d## dimensions using the method of separation of...
  11. wood

    Time independent Schrodinger equation and uncertainty in x

    Homework Statement Is the gaussian $$\sqrt{\frac{\pi}{2\alpha}}e^{-\alpha x^{2}}$$ an eigenfunction of ## \widehat{T} = \frac{\hat{p}^{2}}{2m}## ? If so, what is the corresponding eigenvalue? If not, find a P.E. operator ##\widehat{U} = U(\hat{x}) ## which gives rise to a Hamiltonian...
  12. S

    Solving the Schödinger equation - R.Shankar's PQM, mistake?

    Hello! On p.145 of Shankar's Principles of Quantum Mechanics, the author derives the general propagator for the Schrodinger equation in the following manner. Shankar's working Expanding the state vector in the energy basis, |\psi(t)\rangle = \sum_{E} |E\rangle \langle E| \psi(t) \rangle...
  13. AL-Hassan Naser

    Free electron or empty lattice schrodinger equation solution

    in the solution for free electron we start with X(x) = A exp (ikx) + B exp (-ikx) then using boundary conditions we eliminate B if the wave is traveling in the positive direction and vice versa my questions are: 1. what is the boundary condition used? 2. is it X(-inf) = 0? because this would...
  14. M

    Python Python, solving Schrodinger equation using Runge-Kutta

    Homework Statement I'm currently working on a project in which I have to solve the energy eigenvalues of the Schrodinger equation to compute the mass of certain Mesons. We've been taught very little programming (so apologies that my understanding is very basic), and are therefore given any...
  15. J

    Relativistic correction of Schrödinger equation

    Hello there, I've been given the relativistic correction of the Schrödinger equation for a free particle: $$ - \frac{\hbar^2}{2m} \frac{\partial ^2\Psi}{\partial x^2} - \frac{\hbar^4}{8m^3c^2} \frac{\partial ^4\Psi}{\partial x^4} + E_0 \Psi = i \hbar \frac{\partial \Psi}{\partial t} $$ How we...
  16. C

    Numerical solution to Schrödinger equation - eigenvalues

    Not sure whether to post this here or in QM: I trying to numerically solve the Schrödinger equation for the Woods-Saxon Potential and find the energy eigenvalues and eigenfucnctions but I am confused about how exactly the eigenvalues come about. I've solved some differential equations in the...
  17. Rimmonin

    Is there a space-independent Schrödinger equation?

    I'm learning about the Schrödinger equation in one of my uni courses, and we've recently gone past how to solve the time-independent version. That got me wondering if there is a space-independent version of the Schrödinger equation and what it could possibly be used for. I know I'm probably...
  18. H

    What does the wavevector "k" mean in the Schrödinger eq. ?

    why the solution for energy levels of electron in 1D crystal lattice as solved in Kronig penny model has used wave vector k differently then the Schrödinger equation solved for a free particle. (only the conditions in the equation has changed not the maths...so the "USE" of wavevector 'k' must...
  19. U

    Energy on the RHS of Schrodinger wave equation

    Hi, So in the steady state Schrodinger equation (SE), the E on the RHS (see http://scienceworld.wolfram.com/physics/SchroedingerEquation.html) is the sum of the kinetic and potential energy of the electron. However, is this the same as the 'internal energy'? The statistical distribution used...
  20. gfd43tg

    Time independent schrödinger equation query

    Hello, the TISE can be simplified $$H \psi = E \psi$$ Where ##H## is the Hamiltonian, and ##E## is the eigenvalue, but why don't the ##\psi## terms cancel, leaving ##H = E##? Also, what the heck does the eigenvalue ##E## have to do with the eigenvalue that I have previously encountered in...
  21. kini.Amith

    Separation of variables to solve Schrodinger equation

    How do we know that separable solutions of Schrodinger equation (in 3d) form a complete basis? I understand that the SE is a linear PDE and therefore every linear combination of the separable solutions will also be a solution , but how do we know that the converse, i.e 'every solution can be...
  22. T

    How can the Schrodinger equation be applied to a 3D rectangular box?

    Can anyone give me a really simple example on how to use the eqn above to solve it?
  23. P

    Wavefunctions that don't satisfy Schrödinger equation

    If there exists some normalized wavefunction ##\psi## that is not a solution to the Schrödinger equation (1D), what does this mean? You can still presumably use the square of the wave function to ascertain the probability it exists at some interval in space, but does it provide any other useful...
  24. S

    Boundary Conditions for Hydrogen Schrodinger Equation

    If I am trying to derive the energy eigenvalues and quantum numbers for the hydrogen atom (basic hydrogen-1), I obviously need to solve the hydrogen Schrodinger equation and account for some boundary conditions. However, no website ever gives me the boundary conditions. What would be the...
  25. P

    Question about the Hamiltonian Operator

    In my physical chemistry course, we are learning about the Schrödinger Equation and were introduced to the Hamiltonian Operator recently. We started out with the simple scenario of a particle in 1D space. Our professor's slide showed the following "derivation" to arrive at the expression for the...
  26. hunc

    How Is the Schrödinger Equation Derived from the Hamilton-Jacobi Equation?

    Homework Statement I am reading Mathematical Concepts of Quantum Mechanics (Stephen J. Gustafson, Israel Michael Sigal. Second edition). The book would like to find an evolution equation which would lead to the Hamilton-Jacobi equation $$\frac{\partial S}{\partial t}=-h(x, \nabla S) $$ in the...
  27. R

    Time-independent Schrodinger equation in term of the TDSE

    Homework Statement Write down the general solution of the time-dependant schrodinger equation in terms of the solutions of the time-independant Schrodinger equation. Homework Equations TDSE TISE The Attempt at a Solution I'm really not sure how to interpret this question, I could write the...
  28. Ahmad Kishki

    Thinking about the Schrodinger wave equation

    so H(psi) = E(psi) is the schrodinger equation such that psi is the eigen function of the hamiltonian operator, and since E is the eigen value of the hamiltonian, then this E is the measured E. This is what i understand so far, and i am building on this here. All psi must be eigen function of...
  29. Chemer

    Solving of schrodinger's wave equation

    It's the application of Shrodinger wave equation to H-atom and I can't solve the first step. Please help me solve this. I'm not maths student so it's really hard to solve it:( d^2 psi/dx^2+d^2psi/dy^2+d^2psi/dz^2+8π^2m/h^2(E-V)=0 Where x= rsin(theta)cos(phi) y=rsin(theta)sin(phi) z=rcos(theta)...
  30. Paradox101

    Schrödinger's time-dependent equation (general)

    The Hamiltonian operator in the equation i×h/2π×∂/∂t×ψ=H×ψ(where 'i' is the imaginary no.,'h/2π' is just expanded form of the reduced Planck constant,'∂/∂t' is the partial derivative with respect to time 't' and ψ is the wave function) is,as I recall,H=I+V(i don't know how to get those carets...
  31. P

    Show that the function satisfies the Schrodinger eqaution

    Homework Statement So I am quite new to quantum mechanics and i am self teaching through a book called "Quantum mechanics for applied physics and engineering" by Albert Thomas Fromhold Jr. There are no solutions to the exercises, I am im not sure how to begin with these types of questions...
  32. B

    Need help with Schrödinger and some integration

    My wave function: ##\psi_2=N_2 (4y^2-1) e^{-y^2/2}.## Definition of some parts in the wavefunction ##y=x/a##, ##a= \left( \frac{\hbar}{mk} \right)##, ##N_2 = \sqrt{\frac{1}{8a\sqrt{\pi}}}## and x has an arrange from ##\pm 20\cdot 10^{-12}##. Here is my integral: ##<x^2> =...
  33. G

    Method for deduce Schrödinger Equation

    Is there any method for deduce Schrödinger equation from quantization of action??
  34. B

    Solution to the Schrodinger Equation

    Homework Statement Consider the full 1-electron hydrogen wave function. [/B] Prove that ψ =A(6r –r2/a0) exp[-^r3/a0] sinθ exp[+iφ], is a solution to the Schrodinger equation H|ψ> = E|ψ>, where H is the Hamiltonian operator. Hence show that it's energy E= -1.51 eV and its principle quantum...
  35. S

    Renormalisation of the Schrodinger equation

    Hi, I am a senior year Physics undergraduate and my current understanding of quantum mechanics stands at the level of the Griffiths textbook. I am trying to understand what it means to renormalise the Schrodinger Equation. I know that it's not possible to understand the detailed mathematics of...
  36. Z

    Is there any explanation of Josephson effect based on Schrodinger equation?

    All explanations of Josephson effect I have read so far are based on Ginzburg–Landau theory. There seems no explanation based on Schrodinger equation. Why? While an explanation of Josephson frequency of 2eV/h seems not difficult to envisage, the major problem, I guess, should be with electron...
  37. A

    Solution to the Schrödinger equation for a non rigid step

    I've been having troubles resolving the Schödinger's time independent one-dimensional equation when you have a particle that goes from a zone with a constant potential to a zone with another constant potential, yet the potential is a continuos function of the form: $$ V(x)=\left\{...
  38. C

    Adjoint of Schrodinger Equation

    I'm missing something obvious so please point out what I'm thinking wrong SE equation is: ih d/dt |> = H|> the taking adjoint turns i -> -i and (d/dt) -> -(d/dt) so adjoint of SE should be same as SE however it isn't. adjoint of SE is -ih d/dt |> = H|> do we not take adjoint of d/dt, if...
  39. M

    Solutions of schrodinger equation contradicts HUP

    By solving the schrodinger equation, we get atmost two solutions for wavefunctions with definite wavenumber and definite wavelength. Thus, we know specifically the momentum of the particle. But this is contradicted by HUP. Please explain. I would appreciate an explanation in the context of a...
  40. Erland

    Schrödinger Equation in the classical limit

    I am currently trying to learn a little about quantum mechanics, although not on very detailed level. There is one thing I wonder: What happens with the Schrödinger Equation in the classical limit, i.e. when either the mass of the particle tends to infinity or when Planck's constant tends to 0...
  41. V

    Galilei Transformation Free Schrödinger Equation

    Homework Statement I am supposed to show that the free Schrödinger Equation is NOT kovariant under Galilei Transformation. Homework Equations We learned in Lectures that the Galilei Transformation can be written as: \vec{x'}=\hat{R}\vec{x}-\vec{a}-\vec{v}t (1) or equivalently...
  42. V

    On nonlinearity parameter in Nonlinear Schrodinger Equation (NLS)

    While I am studying the wave propagation in fluids, the amplitude modulation seems to be governed by the Nonlinear Schrodinger (NLS) equation. In some of the journal papers the nonlinearity parameter, N seems to be of high value (N≈O(104)) and so on. I understand that weak nonlinearity...
  43. moriheru

    Exploring Dimensions: The 4D Schrodinger Equation Made Simple

    This is a rather naive question concerning the dimension of the schrodinger equation. If the Schrodinger equation can be wrtiten in a three dimensional form using the laplacian operator can it be written in a 4d version. I understand that the schrodinger equation shows the development of the...
  44. W

    Schrodinger in a weak periodic potential

    Hi, I have problems figuring out what both c-coefficients means. Can someone explain this in a conceptual way? Also, Vg and V-g are the coefficients of the Fourier series if you expand V, but what does it mean physically? Thanks in advance.
  45. B

    Schrodinger equation with unknown potential function

    How to find wave function if potential function is unknown. I have only the scattering data: time and coordinates of scattering particle.
  46. S

    Schrodinger wave eqn for a beam of monoenergeticc electrons

    The problem is to apply Schrodinger wave equation to a beam of mono energetic electrons and show that the probability of finding electron at each point on the beam is constant (d2ψ/dx2) + (8∏^2m/h^2)(E-V)ψ = 0 I have been taught to apply this to a single particle for various...
  47. Q

    Different forms of Schrodinger equation

    I got confused when in my book they went from one form of schrodinger equation to another. It doesn't make much sense to me algebraically, probably i have some lacks in complex numbers. Here are the equations: In the second one I think it's implied that above two equations give third and I...
  48. D

    Any quick help with rearranging schrodinger equation in dirac notation

    I'm looking through my lecture notes, (studying relativistic corrections/perturbation theory using hydrogen), and I seem to have a mind block with one of the equations (the last one from the 3 in the middle). I know that the kinetic energy and coulomb potential has been subbed in for the...
  49. S

    Erwin Schrödinger Ghost Particles & Energy of Molecules & Atoms?

    Hello there. I did research on some of Schrodinger work. My question is the transfer of Energy between the Atoms and Molecule. Schrodinger made an analogy with the Cat/Atom Scenario but the real particle in question is the NH2 Mole & H-Atoms with ghost energy being observed. The reason I read...
  50. ShayanJ

    Non-dimensionalization of Schrodinger equation

    I had a course of computational physics in university. When the professor wanted to non-dimensiolize the Schrodinger equation, among other things, he changed the wave function using the relation |\psi(x)|^2 dx=|\phi(y)|^2 dy where y is the non-dimensionalized postion (y=\frac x a) and so...
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