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. mangojuice14

    Identical particles and separating the Schrodinger equation

    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...
  2. B

    I About general solutions to 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...
  3. P

    Solve time-dependent Schrodinger equation for V=V(x,t)

    Homework Statement For the potential ##V(x,t) = scos(\omega t)\delta (x) ## where s is the strength of the potential, find the equations obeyed by ##\phi_n(x)## And again for ##V(x,t) = \frac{\hbar^2}{2m} s \delta(x - acos(\omega t))## Homework Equations Time-Dependent Schro: ##...
  4. E

    A Is my solution of time-dependent Schrodinger equation right?

    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...
  5. A

    I Numerical solution of Schrödinger equation

    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...
  6. M

    Solving Radial Schrodinger Equation

    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...
  7. A

    I Finite difference method for Schrödinger equation

    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...
  8. Mayan Fung

    Physical interpretation of Schrodinger equation

    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...
  9. A

    I How to discretize the Schrödinger equation with spin

    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...
  10. I

    I How to turn model of Schrödinger's Equation 2D?

    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...
  11. N

    B Any good lay explanation of the Schrödinger cat duality?

    Once again, I came across the notion (in a lay physics book by an academic) that two mutually exclusive states simultaneously exist until observed (based on the Schrödinger living/dead cat thought experiment), which, on its face, seems to me to belong to theology and not to science. That both...
  12. J

    I Just to check Schrodinger equation with 2 electrons

    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...
  13. gimak

    Time independent schrodinger equation

    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 ?
  14. DiracPool

    B Dirac Equation vs. Schrodinger Equation

    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...
  15. F

    I Feynman Lectures: negative alpha for solving Schrödinger equation

    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) ?
  16. G

    B Schrodinger cat superperposition vs sharp state

    On the Schrodinger cat, can I simply say, outside the box,the state is in superposition,but inside the box, the state is not. Besides, the experiment is so simple to do, how come no body ever did it ?. Just put an animal you hate or even an inset, and observe the expected (50% -50%) result...
  17. Q

    I Schrodinger equation in terms of complex conjugate

    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
  18. D

    I Quantum Superposition While Observing Phenomena?

    I decided to perform a little thought experiment -- without the mathematics. Assume we have two Schrodingers' Cats. After a while, they will be in a superposition of being alive and dead at the same time. Now assume that they are entangled, and we open the boxes at the exact same time. Cases...
  19. T

    I Schrödinger equation and interaction Hamiltonian

    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...
  20. M

    Schrodinger equation for a weird potential

    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...
  21. J

    I Why don't we use the Schrodinger Uncertainty Principle?

    I have read that the Schrodinger Uncertainty Principle is an extension of Heisenberg's. So, why don't we use the Schrodinger Uncertainty Principle instead of Heisenberg's? Thanks!
  22. A

    Schrödinger Equation: Solving for Energy in a Semi-Infinite Square Well"

    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...
  23. G

    I Schrödinger Potential Fields with no Energy Quantisation?

    The solution to the One-Dimensional Time-Independent Schrödinger equation for an electric potential field of constant value is an exponential function, and its energy eigenvalue can have any value, it is not quantised. Are there any other potential field functions whereby the energy of the...
  24. S

    A Integration of Schrodinger equation

    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...
  25. R

    A The Nonlinear Schrödinger Equation

    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}...
  26. J

    Angular momentum of hydrogen atom with Schrodinger Equation

    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...
  27. K

    Schrodinger Equation/verify solution

    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...
  28. amjad-sh

    I Schrodinger equation and stationary states

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

    A Time correlation of an observable in the Schrödinger picture

    This has come up in a number of threads, so I made this thread to talk about it. I think that an interpretation of this in the Schrödinger picture should be possible at least in the style of Feynman. This would go something like this. ##\begin{eqnarray*} \langle A(s)A(t)\rangle_\psi &=&...
  30. Z

    Are All Solutions of the 1D Schrodinger Equation Energy Eigenstates?

    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)
  31. Schwarzschild90

    Planar wave solution to zero potential Schrödinger equation

    Homework Statement Homework Equations \begin{align} \begin{split} \psi(x, t) = e^{(ikx- i \omega t)} \\ V(x) = 0 \end{split} \end{align} The Attempt at a Solution For a free particle, the Schrödinger equation can be put in the form of ##\psi(x, t) = e^{(ikx- i \omega t)}##...
  32. A

    How Can We Calculate Band Bending Using Schrödinger-Poisson Theory?

    I am reading a lot about how to calculate band bending from solving the Schrödinger equation and Poisson equation self-consistently. To recap some of the central ideas are: We look at the conduction band of some semiconductor. If we assume that the electrons are free electrons with some...
  33. Konte

    Variable separation - Schrödinger equation

    Hello everybody, My question is about variable separation applied in the solution of general time-independent Schrodinger equation, expressed with spherical coordinates as: \hat{H} \psi (r,\theta,\phi) = E \psi (r,\theta,\phi) Is it always possible (theoretically) to seek a solution such as...
  34. W

    Schrodinger equation for potential step

    Homework Statement There is a stream of electrons with energy E, incident from x = -∞ on a potential step such that V(x) = ##V_{0}## for x<0 and 0 for x>0. E>##V_{0}##>0. Write the T.I.S.E for x<0 and x>0 and find the general solution for both. Homework EquationsThe Attempt at a Solution My...
  35. phinds

    Pavlov & Schrodinger: A Study of Influential Scientists

  36. naima

    What is the law for probability having Schrodinger equation?

    I think that all is in the title. If the amplitude ##\phi## obeys a Schrodinger equation, what is the law for ##p = \phi^* \phi##?
  37. T

    News Planck, Schrodinger, and what to do during political catastr

    When I was young I read Schrodinger's memoirs. I can't find a book, but I remember he described an interesting conversation with Max Planck about what to do during the political catastrophe. The conversation was in 1940, and Schrodinger was asking Planck's opinion on what to do - to immigrate...
  38. naima

    Is Fokker Planck equation equivalent to Schrodinger equation

    I found this question here but i do not understand the answer. One equation is from classical physics and the other from quantum physics. Is there another way to go from classical to quantics than the analytical extension?
  39. W

    How can the Schrodinger equation be used to solve a potential symmetry problem?

    Homework Statement (See attached photo) Homework EquationsThe Attempt at a Solution I Have no clue where to start for b), i need major help! For a I said that you can argue since the potential is symetric along the x-axis that this operator will go to 0. However I don't know where to start for...
  40. W

    Schrodinger equation in a well question?

    Homework Statement (See attached picture) Homework EquationsThe Attempt at a Solution I'm not even sure where to start :( I'm assuming that i have to find a wave function outside and inside the well and meet certain boundary conditions, but I am confused. Please help.
  41. M

    Time Independent Schrodinger Equation

    Homework Statement Verify that a plane wave ψ(x) = Ae-ikx is a solution to the time independent Schrodinger equation for a free particle in one dimension. Can it be normalised? Why?[/B]Homework EquationsThe Attempt at a Solution My lecturer's notes are all over the place, which is frustrating...
  42. RJLiberator

    How Does the Time-Dependent Schrödinger Equation Describe Qubit Evolution?

    Homework Statement Let |v(t)> ∈ℂ^2 by the time-evolving state of a qubit. If |v(0)> =\begin{pmatrix} 0 \\ 1 \end{pmatrix} , and the Hamiltonian of the system is H = \begin{pmatrix} 0 & -iλ \\ iλ & 0 \end{pmatrix} (where λ∈ℝ) what is |v(t)>?Homework Equations Time dependent schrodinger...
  43. Jarrodmccarthy

    Does Quantum Contextuality only apply to spin?

    I have just recently started learning about quantum contextuality and can only seem to find examples where contextuality is need to explain measurements of spin. So I am curious as to whether quantum contextuality only applies to measurements of spin? Also, If someone could clarify where the...
  44. A

    Schrodinger equation for step potential

    Homework Statement Consider the one-dimensional Schrodinger equation for the step potential, that is for U(x) = 0 for x<0, and for , . Consider a particle with mass m and energy E < U. Assume the particle is initially at x<0. a) Calculate the penetration depth Δx at which the probability...
  45. S

    Solution of Schrodinger equation in axially symmetric case

    The following extract is taken from Appendix A of the following paper: http://arxiv.org/abs/0810.0713.Any solution of the Schrodinger equation with rotational invariance around the ##z##-axis can be expanded as ##\psi_{k}=\Sigma_{l}A_{l}P_{l}(cos \theta)R_{kl}(r)##, where ##R_{kl}(r)## are the...
  46. A

    How to Separate Variables for the Schrodinger Equation in Two Dimensions?

    Homework Statement Consider the time-dependent Schrodinger equation for a free particle in two spatial dimensions Using the method of separation of variables, determine the wave function ψ(x,y,t) Homework EquationsThe Attempt at a Solution Not sure how to do the separation here since it is...
  47. entropy1

    Depiction of distribution of photons over time

    I have a question about photons and the Schrödinger equation. Photons behave like particles but also as waves. I understand that this can be described by the Schrödinger equation as a photon having a certain probability to be somewhere. If I understand this correctly, I take it that there are...
  48. D

    Griffiths Quantum Question. Unit-less Schrodinger Equation.

    In Grifftiths Intro to Quantum 2nd edition, page 51, he is re-expressing the Schrodinger equation for a harmonic oscillator in terms of a unit-less quantity \xi \equiv \sqrt{\frac{m\omega}{\hbar}}x So Griffiths takes the Schrodinger equation in equation [2.70] -\frac{\hbar^2}{2m}...
  49. A

    Finite difference Schrodinger equation

    I am simulating electrons inside a cylindrical well like the one shown on the first figure. My current work has been on solving the Schrodinger equation numerically for the above potential and then finding corrections to the solution such that it is consistent with Poissons equation. To do so...
  50. PhysicsKid0123

    Time dependent schrodinger equation and wave function

    1. Homework Statement p: momentum x: position t: time h_bar: Planck's constant Ψ: wave function Homework Equations The Attempt at a Solution I've posted a link to pictures. http://imgur.com/a/TKvUu I'm not vera good at using LaTex yet :( So I've shown that the wave equation satisfied the...
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