What is Schrodinger equation: Definition and 564 Discussions

The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of the subject. The equation is named after Erwin Schrödinger, who postulated the equation in 1925, and published it in 1926, forming the basis for the work that resulted in his Nobel Prize in Physics in 1933.Conceptually, the Schrödinger equation is the quantum counterpart of Newton's second law in classical mechanics. Given a set of known initial conditions, Newton's second law makes a mathematical prediction as to what path a given physical system will take over time. The Schrödinger equation gives the evolution over time of a wave function, the quantum-mechanical characterization of an isolated physical system. The equation can be derived from the fact that the time-evolution operator must be unitary, and must therefore be generated by the exponential of a self-adjoint operator, which is the quantum Hamiltonian.
The Schrödinger equation is not the only way to study quantum mechanical systems and make predictions. The other formulations of quantum mechanics include matrix mechanics, introduced by Werner Heisenberg, and the path integral formulation, developed chiefly by Richard Feynman. Paul Dirac incorporated matrix mechanics and the Schrödinger equation into a single formulation. When these approaches are compared, the use of the Schrödinger equation is sometimes called "wave mechanics".

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  1. V

    Solving the Schrodinger Equation Using Substitution Method: Tips and Tricks

    I tried simply substituting z and epsilon into the original equation. I managed to get the second term of the left hand side correct but not the first term as I don't know how to turn z into d^2/dz^2. Can you please give me suggestions as to how I can approach this question. Thanks
  2. G

    Time-Dependent Perturbations in Schrodinger Equation

    From what I see, the time dependence in potentials do not change the spatial aspect of the wave function. They contribute a time dependence to the population of what were originally stationary states. If this is the case, then does that imply that the time independent bases are the ones we...
  3. B

    Harmonic oscillator verify both solutions to schrodinger equation

    Homework Statement a particle of mass m moving in one dimension has potential energy V(x)=0.5m [[omega(subscript0)]^2] x^2 verify that psi0 (proportional to) exp [(-m omega0 x^2)/2 h bar] and psi1 (proportional to) exp [(-m omega0 x^2)/2 h bar] are both solutions of the time...
  4. G

    Schrödinger equation with spin term

    hi, can anybody of you show me how the schrödinger equation with the spin term of the electron for the hydrogen atom looks like? i really do not know how to do this Gavroy
  5. P

    Why is this NOT a solution to the time independent Schrodinger equation.

    Homework Statement Given a set of solutions |psi_n> to the TISE show that a) |Capital-psi>=Sum(C_n|psi_n>) is not a solution to the TISE Homework Equations ***H|psi_n>=E_n|psi_n> The Attempt at a Solution I don't really know where to start, I plugged |psi_n> into *** and I am...
  6. M

    Time Independent Schrödinger equation.

    Pardon my ignorance but why does the Time Independent Schrödinger equation use Time? It uses a kinetic energy operator. Kinetic energy; "It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity." Velocity is; "The scalar absolute value...
  7. S

    Solving the Schrodinger equation

    This extract is from my college notes. "Because of the inherent difficulty of obtaining even grossly approximate solutions of the complete Schrodinger equation, one typically focuses on reduced formulations that are believed to capture the essential features of the problem of interest. This...
  8. B

    Showing Superposition Principle with Time-Dependent Schrödinger Equation

    Homework Statement Show that, if psi1 and psi2 are both solutions of the time-dependent Schr¨odinger equation, so is c(subscipt1) psi1 + c(subscript2) psi2 (where c1 and c2 are arbitrary constants). Homework Equations The Attempt at a Solution every source I've consulted so far...
  9. P

    Why the Integration Constant in the Schrödinger Equation is Set to L(L+1)?

    in the schrodinger equation the integration constant in the angular wave equation is set to L(L+1). may i know why this is set ,what is the reason , thx!
  10. K

    Prove this function satisfies the time independent schrodinger equation

    Prove this function satisfies the time independent schrodinger equation. When V is constant. Psi = A e^(i k x) + B e^(-i k x) Attempt: Time independent schrodinger equation : (- (hbar^2) / 2m) * (d^2 Psi / d x^2) + V Psi = E Psi Second order derivative of Psi : (-k^2 A e^(i k x)) + (-...
  11. C

    Solving Schrodinger Equation: xav, (x2)av, Δx

    Homework Statement Use the ground-state wave function of the simple harmonic oscillator to find xav, (x2)av, and \Delta x. Use the normalization constant A=(\frac{m\omega _0}{\overline{h} \pi })^{1/4}Homework Equations \psi (x) = Asin(kx) (f(x))_{av} = \int ^{\infty }_{-\infty } \left| \psi (x)...
  12. E

    Minimum Momentum and Energy from Schrödinger Equation

    Homework Statement I have a 2D square well with sides a. What is the minimum momentum and energy for this well? Homework Equations Minimum momentum given by Δp≈ℏΔx and Δp≈ℏΔy Minimum energy given by ΔE≈ℏΔt This might be right. It says to consider the Schrödinger Equation in 2D. I've never...
  13. A

    Positronium, Hydrogen, Schrodinger Equation

    I have been studying QM and am interested in keeping to the non-relativistic theory for now. In many experiments of crossed gamma rays in the vicinity of a massive particle (or nucleus), pair generation of an electron and its anti-particle the positron is well described. In some instances, the...
  14. T

    Schrodinger equation solution when U>E

    Homework Statement see attachment Homework Equations TISEThe Attempt at a Solution a)When U>E -\frac{\hbar^2}{2m}\frac{d^2\Psi(x,t)}{d x^2}+U(x)\Psi(x)=E\Psi(x) leads to blahblahblah...(there is only transmittion no reflection as x to infty) \Psi(x)=Be^{-\alpha x}, where \alpha =...
  15. M

    Schrodinger Equation : Infinite Square Well

    Hi, I am having trouble understanding an example from a textbook I am reading on the Schrodinger equation. The example deals with an infinite square well in one dimension. With the following properties: V = 0\,where -a \leq x \leq a V = \infty\,|x| \geq a Where V is the potential. The...
  16. C

    Time-Independent Schrödinger Equation

    How can time-independent schrödinger equation be proven? Do you know any source which explains it clearly? Thanks for replies.
  17. C

    Hydrogen atom with discrete nonlinear Schrödinger equation

    Hi everyone, How can I solve hydrogen atom with discrete nonlinear schrödinger equation? Could you help me with the mathematics of that, please?
  18. H

    How Does the Schrödinger Equation Account for Rest Mass Energy?

    i know its a stupid question but I am a beginner: according to eisntein: E=K+m_{o}c^2 but the plane wave solution yields that particle's KE is its total energy,where free particle has no potential energy. But where is the rest mass energym_{o}c^2? Is it omitted?
  19. K

    What does Schrödinger equation prove/mean?

    1. I am writing one page on if there is free will(using physics). I concluded that there is no free will and I am trying to use Schrödinger equation in my paper, but i don't understand what its proving/means. And if possible can i get an example that will prove the equation(no math, just an...
  20. M

    Schrodinger Equation a constant?

    Im new to all of this a just started studying quantum mechanics and the time-dependent schrodinger equation. What attributes must be known of a particle to use the schrodinger equation? Also is the wave function considered a constant?
  21. J

    About the Schrodinger equation, the Hamiltonian, time evolution?

    Forgive me if this is a poorly asked question but I am not yet completely fluent in quantum mechanics and was just looking at the energy eigenvalue equation H|\Psi\rangle = i\hbar \frac{\partial}{\partial t}|\Psi\rangle = E|\Psi\rangle . We've got the Hamiltonian operator H acting on the state...
  22. 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
  23. 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...
  24. 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...
  25. 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...
  26. 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...
  27. 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?
  28. 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...
  29. 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
  30. 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...
  31. 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.
  32. 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...
  33. 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...
  34. 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...
  35. 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) =...
  36. 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...
  37. 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...
  38. 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...
  39. P

    Obtaining schrodinger equation

    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...
  40. 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...
  41. 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...
  42. 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...
  43. 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...
  44. 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
  45. 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
  46. 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...
  47. 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,->...
  48. 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...
  49. 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...
  50. 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...
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