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. N

    Original Schrodinger Equation Article in English

    Hi every one .. Could anyone provide me a link of original schrodinger equation article in english?? I'll really approciate that
  2. L

    Time independant schrodinger equation

    Homework Statement Write down the time independant schrodinger equation in the momentum representation for a particle with mass m when the potential is given by V (x) = 1/2 \gamma x2. A possible soloution of this schrodinger equation is of the form \Psi (p) = Ae-Bp2 / 2 Determine...
  3. diegzumillo

    2d Schrodinger equation - numerical solutions

    Hi there, I was expecting to find a "simulations forums" somewhere here, if there is a better place for this thread please let me know :) OK, here's the problem: I'm trying to make a simulation with PYthon, at first with a square potential, for simpler potential/boundary conditions. But...
  4. M

    Simple question on Schrodinger Eqn

    I take Schrödinger Equation and look for spherically symmetric stationary state wave function. I make substitution \sigma (r) = r X(x) get simpler form. This equation is defined for r \geq 0 , Boundary Conditions is that wavefunction is finite at all points. Now It is possible to relate nicely...
  5. W

    What does it mean to satisfy the Schrodinger equation?

    What does it mean to "satisfy" the Schrodinger equation? Homework Statement Show that the 2p wave functions of the hydrogen atom satisfy the radial Schrodinger eq. One of the radial equations for the 2p state is \frac{1}{\sqrt{96 \pi a^{3}}} \frac{r}{a} e^{\frac{-r}{2a}} Homework Equations...
  6. W

    Show that R satisfies the radial Schrodinger equation

    Homework Statement Starting with \psi(r,\theta,\phi)=R(r)Y(\theta,\phi) saubstitute into the Schrodinger equation and show (using the technique of separation of variables) that R satisfies: (\frac{\hbar^2}{2m}\frac{1}{r^2}\frac{d}{dr}(r^2\frac{d}{dr})+\frac{C}{2mr^2}+V(r))R=ER(r) Homework...
  7. S

    Solve Schrödinger Equation: Need Help

    Homework Statement Hi, I've just started this new course about quantum mechanics and it begins, among others, with this question: [PLAIN]http://img710.imageshack.us/img710/2962/unbenanntfwg.jpg I'm really at a loss how to approach this one. Can anyone please help?
  8. kreil

    Green's Function in Time-Dep. Schrodinger Eqn.

    Show, from it's definition, \psi(x,t) = \int dx' G(x,t;x',t_0) \psi(x',t_0) G(x,t;x',t_0)= \langle x | U(t,t_0) | x' \rangle that the propagator G(x,t;x',t') is the Green Function of the Time-Dependent Schrodinger Equation, \left ( H_x - i \hbar \frac{\partial}{\partial t} \right )...
  9. F

    Schrodinger Equation for Potential Well

    Homework Statement A particle of mass m and total energy E < 0 is confined to a potential given by: where \alpha is some positive constant. Show that the wavefunction is a solution of the time independent Schrodinger equation when x > 0. Find the associated energy Eigenvalue E.Homework...
  10. D

    General solution of Schrodinger eq. proof

    Homework Statement Let |\psi\rangle and |\psi '\rangle be solutions to the same Schrodinger equation. Show than, that c|\psi\rangle+c'|\psi '\rangle is the solution, where c and c' are arbitrary complex coefficients, for which holds: |c|^2+|c'|^2=1 The Attempt at a Solution Now this follows...
  11. L

    No charge of particle in Schrodinger Equation

    Why does charge of a particle not appear in Schrodinger Equation even though mass appears? Chapter 5 Q No. 9 Quantum Physics of Atoms Molecules Solids Nuclei and Particles - Robert Resnick, Robert Eisberg
  12. B

    Solving Schrodinger Equation for Modified Stepwise Potential

    Homework Statement Consider reflection from a step potential of height V0 with E > V0, but now with an infinitely high wall added at a distance a from the step (x=0 at V=V0) Solve the Schrodinger equation to find \varphi(x) for x<0 and 0 \leq x \leq a. Your soultion should contain only one...
  13. W

    Schrodinger ground state wave function

    Homework Statement Find the ground state wave function for the 1-D particle in a box if V = 0 between x = -a/2 and x = a/2 and V = \infty Homework Equations I would guess -- Schrodinger's time-independent equation...
  14. X

    Potential function for the Time-Independent Schrodinger eq.

    Homework Statement [PLAIN]http://img820.imageshack.us/img820/4205/agvg.png Homework Equations TISE: \left(-\frac{\hbar}{2m}\nabla^2 + V(r) \right) \psi(r) = E\psi(r) The Attempt at a Solution Can someone tell me what 'transcendental' means in part b). I've...
  15. X

    Solutions of of the time-independent Schrodinger eq.

    Homework Statement Supposed that \psi1 and \psi2 are two different solutions of the TISE with the same energy E. a) show that \psi1 + \psi2 is also a solution with energy E. b) show that c*\psi1 is also a solution with energy E. Homework Equations TISE: (-\hbar/2m)*\nabla^2*\psi(r)...
  16. C

    Solving Schrodinger Equation with Angular Wavefunction Y1,1

    Can someone help me with this problem? show that the angular wavefunction Y1,1 is a solution to the schrodinger equation.
  17. U

    MATLAB Simulating Schrodinger wave equation using MATLAB.

    Hi! I've just finished learning the basics of MATLAB from an internet tutorial. I know a the basics of how to represent and manipulate vectors,matrices,graphs and plots on MATLAB. Now,my H.O.D wants me to make a programme that will simulate the Schrodinger wave equation on MATLAB...and I...
  18. A

    Probability amplitude in Heisenberg e Schrodinger pictures

    Hi, this is my question: suppose that at time t' our system is in the state | \psi(t')\rangle The probability for the system to be in the state | \phi\rangle at the time t'' is the norm of \langle \phi| \psi(t'')\rangle This in the Schrodinger picture. But how i can write the same thing in...
  19. N

    Heisenberg vs Schrodinger Picture

    Please tell me where my understanding of the Heisenberg and/or the Schrodinger picture falls apart. -Schrodinger says the state vector of a system changes with time according to a unitary operator that doesn't change with time. -Hesienberg says the state vector of a system doesn't change...
  20. E

    Commutator Relations vs. Schrodinger Equation

    Some books begin QM by postulating the Schrodinger equation, and arrive at the rest. Some books begin QM by postulating the commutator relations, and arrive at the rest. Which do you feel is more valid? Or are both equally valid? Is one more physical/mathematical than the other? I...
  21. pellman

    Why isn't the Pauli equation equivalent to the Schrodinger equation?

    The Pauli equation (seen here) contains its spin dependence in the term which reads \frac{1}{2m}\left[ \sigma\cdot\left(p-\frac{e}{c}A\right)\right]^2 So let B be any vector. Then \left( \sigma\cdot B\right)^2 =\left(\sigma_1 B_1 +\sigma_2 B_2 + \sigma_3 B_3\right)\left(\sigma_1 B_1...
  22. H

    Wavefunction obeying Schrodinger equation.

    Homework Statement I've attached my past paper question, which contains the relevant integral identity too. The Attempt at a Solution This question is relatively simple, yet I can't seem to complete it. I used the schrodinger equation which is: -(ħ²/2m)\nabla^2u + Vu = Eu...
  23. H

    General Solution to time independent schrodinger equation

    Homework Statement This is really a maths problem I'm having. I need to get the general solution for the infinite square well in the form: u = A cos(kx) + B sin(kx) I found the general solution to be: u = A exp(ikx) + B exp(-ikx) Using Euler's formula: exp(ikx) =...
  24. H

    Schrodinger Equation: Kinetic Energy Impact?

    I am sure you are all aware of the Schrodinger equation. The Hamiltonian is included in this equations, which contains the Kinetic energy operator. When Schrodinger wrote thi he converted momentum to the unit imaginary number, the reduced Planck constant and the Delta operator. My...
  25. P

    Solving Delta Potential Barrier Problem with Schrodinger Equation

    Homework Statement In delta potential barrier problem Schrodinger equation we get \psi(x)=Ae^{kx}, x<0 \psi(x)=Ae^{-kx}, x>0 We must get solution of lim_{\epsilon \rightarrow 0} \int^{\epsilon}_{-\epsilon}\frac{d^2\psi}{dx^2}dx Homework Equations The Attempt at a Solution lim_{\epsilon...
  26. H

    Schrodinger Time Dependent equation

    Can someone explain the components of the Time dependent Schrodinger equation for me. Thank you -H
  27. G

    Solving Schrodinger Equation for Y(x)=A Sin (x)=0

    ive been asked to show that the function of Y(x) = A sin (x) = 0 is a solution to the equation of d2Y(x) dx2 +k2Y(x)=0 where the Y is meant to be the lowercase wavefunctio psi...i just can't get it to work on this :( basiaclly I am completely...
  28. P

    How Do You Derive the Schrödinger Equation from Classical Expressions?

    Homework Statement Homework Equations This is what I'm trying to obtain, in terms of the elements in the question. Assuming that these 'x' values are 'z'. The Attempt at a Solution I'm not really understanding what it is being asked here. Do I just substitute the value of V(z) into...
  29. G

    Interesting equivalent to Schrödinger equation

    While messing around with the Schrödinger equation on paper, I found an interesting, elegant way of expressing it. Let P be the probability density |\Psi |^2, and let \vec Q be a real-valued vector field. \vec F is a vector field describing the forces acting on the system when in a given...
  30. L

    A Starting with the Schrodinger equation, how do we find the Hamiltonian matrix?

    In his lectures on Quantum Physics, Richard Feynman derives the Hamiltonian matrix as an instantaneous amplitude transition matrix for the operator that does nothing except wait a little while for time to pass.(Chapter 8 book3) The instantaneous rate of change of the amplitude that the wave...
  31. V

    Re-arranging the Schrodinger equation

    I just have a small question, In my book it says that the schrodinger equation, i\hbar\frac{\partial\Psi}{\partial t} = \frac{\hbar^2}{2m}\frac{\partial^2\Psi}{\partial x^2} + V\Psi rearranged is, \frac{\partial\Psi}{\partial t} = \frac{i\hbar}{2m}\frac{\partial\Psi ^2...
  32. X

    Interesting facts about Schrödinger?

    I am doing a report and presentation on Erwin Schrödinger in my physics class and I want it to be exciting and interesting. Does anyone have and interesting facts about this great scientist? Not just FACTS, but INTERESTING facts! I have heard that he was quite the ladies man... Thanks! ~Matt
  33. R

    Problem with complex conjugates and the Time Independent Schrodinger equation

    I can understand that if z= a + ib then z*=a - ib, where the definition of the complex conjugate is reversing the sign in front of the imaginary part. I'm now confused about how the complex conjugate works in the TISE. in a stationary state, i\hbar\frac{\partial\Psi}{\partial\\t}= E\Psi...
  34. I

    Schrodinger solution to hamilton-jacobi

    The Hamilton-Jacobi equation \frac{\partial W}{\partial t}+\frac{1}{2m}\left[\left(\frac{\partial W}{\partial x}\right)^2+\left(\frac{\partial W}{\partial y}\right)^2+\left(\frac{\partial W}{\partial z}\right)^2\right] + V(x,y,z) = 0 Can be re-expressed as |\nabla W| = \sqrt{2m(E-V)} by...
  35. I

    A quantity from schrodinger

    In a paper by schrodinger, he uses \Delta_p^\frac{1}{2}, and \Delta_p^{-\frac{1}{2}} in a particular equation: \Delta_p^\frac{1}{2} \sum_l \frac{\partial}{\partial q_l}\left(\Delta_p^{-\frac{1}{2}}\sum_k a_{lk} \frac{\partial \psi}{\partial q_k}\right)+\frac{8\pi^2}{h^2}(E-V)\psi = 0...
  36. N

    Separation of Schrodinger Equation

    Homework Statement Show that the time-dependent Schrodinger equation is separable when V depends on time only and is uniform in space (i.e., V = V (t)). Homework Equations The Attempt at a Solution In the attached document
  37. S

    Seperation of variables in the Schrodinger equation

    hey guys first post so sorry if this has already been asked :S what exactly is meant by the separation of variables in the schrodinger equation? also what co-ordinate system would i use to solve for an electron in a hydrogen-like ion? thanks
  38. G

    Which algebra vectors satisfy this (Trying to derive Schrödinger)

    Hi, I was wondering why the wave-function in quantum mechanics is complex. There are a lot of threads in the physics section and I've downloaded a lot of papers, but they seem quite technical. So I'd like to examine the following idea (sorry if I use sloppy terms ;) ): I have an orthonormal...
  39. O

    Correspondence betw. Hamilton-Jacobi & Schrödinger eqns.

    Hey everyone, I'm trying to understand more about the correspondence between classical and quantum physics, in particular the relation between classical mechanics in Hamilton-Jacobi form and the Schrödinger equation. The former can be obtained from quantum theory by plugging \psi=\psi_0...
  40. G

    Schrödinger local and deterministic?

    There have been many QM Interpretation thread, but I haven't found this question answered: Taking aside the fact that a complex probability amplitude is not something we can picture, is the Schrödinger equation local and deterministic at once?
  41. Q

    Schrodinger equation and hydrogen atom

    Homework Statement Find the width L of a one-dimensional box for which n=5 level would correspond to the absolute value of the n=3 state of a hydrogen atom Homework Equations am i suppose to use n2h2/8mL2 where n=5 to equate it to the n=3 state of the hydrogen atom? which is -13.6eV/32...
  42. B

    Propagator for a free particle / schrodinger equation

    http://img18.imageshack.us/img18/4295/eqn.png here is the text preceding the exercise: http://yfrog.com/5mch5p in the exercise, where does the factor \frac{m}{(2mE)^{1/2}} come from? Comparing that equation with 5.19 (bottom right of link), why can't we just replace |p> with |E,+> and |E,->...
  43. P

    Dimensionless equation schrodinger with field magnetic

    I can not transform the dimensional Schrodinger equation in dimensionless, please help! -\frac{i\hbar^2}{2m}(\nabla-\frac{ieA}{c})^2\psi=E\psi A=(x\^y-y\^x)\frac{H_{0}}{2} I'm trying to leave it like that: (\nabla-A)^2\psi=E\psi I do not know if I'm posting this in the...
  44. P

    Finding \Psi(x,t) From Schrodinger Equation

    hi is there any way we can find \Psi(x,t) for a given \psi(x,0) ? i got stuck with schrodinger equation...
  45. L

    Solving the Schrödinger Equation for a Step Potential

    Hi everybody! I'm studying the simple case of the solution of the Schrodinger equation for a step potential "[URL .[/URL] As my professor states , the transmission coefficient is 0 when the energy of the particle is E<V. I really don't get how this result is not a contradiction with the fact...
  46. V

    Solving 1 electron atom Schrodinger Equation in rectangular coordinates?

    Hi, I'm a physics undergraduate, and I'm having trouble understanding Atomic Physics right now. At first I thought it (the question in the title) is possible, but then I think I got confused with particle in a box. So I refer to textbooks and look for answers in the internet, and confirmed...
  47. E

    Solving 1D 2-particle/2D 1-particle Schrodinger equation

    Hi Most of my work in the past has been on 1D independent particle systems where I use matrix diagonalisation to solve the time-independent Schrodinger equation. How do I go about this for 2D? Or, more accurately, for a two-body wf in 1D? It strikes me as straightforward to construct a...
  48. O

    Schrodinger Eq. & Energies: Are Values Always Positive?

    just a question about the energies associted wuth the schrodinger equation> are the energy values always positive values. I thought that since when the eigenfunctions exist the particle is in a bound state, that the energy should be less than that required to escape a bound state and should be...
  49. O

    Solve Schrodinger Equation for Infinite Square Well - Q1

    Homework Statement I have just started quantum mechanics bacuase i want to prepare for my class starting in march. I must say so far i find it very confusing: I could use some help with this problem and in addition some explanation on the logic of what it all means. i get that this theory...
  50. R

    Solving Schrodinger's Equation: Finite Jumps at Singular Points?

    When solving Schrodinger's eqn. one comes across the expression: \frac{d^2 \psi}{dx^2}=(V-E)\psi where the mass has been chosen to make \frac{\hbar^2}{2m}=1 If V is infinity at some x, then it is said that \frac{d \psi}{dx} can have a finite jump at that x, since \frac{d^2...
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