What is Schrodinger equation: Definition and 567 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".

View More On Wikipedia.org
Recent contents Top users
  1. 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...
  2. 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...
  3. 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...
  4. 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...
  5. 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...
  6. T

    Radial Schrödinger Equation

    Sorry in advance my english, I tried to translate it to english as good as I can Homework Statement When l has its maximum value, the hydrogen atom radial equation has a simple form of R(r) = Arn-1e-r/na0, where a0 is Bohr's radius. Write the respective radial schrödinger equation. Homework...
  7. C

    Simple Harmonic Oscillator - Schrodinger Equation

    Homework Statement One possible solution for the wave function ψn for the simple harmonic oscillator is ψn = A (2*αx2 -1 ) e-αx2/2 where A is a constant. What is the value of the energy level En? Homework Equations The time independent Schrodinger wave equation d2ψ / dx2 =...
  8. P

    Why amplitude squared gives probability / Schrodinger Equation

    We started Quantum Physics in class, and I tried working out the Schrodinger Equation (not mathematically, of course - that's far beyond my level. Just the vague concepts) I understand it's basically a function that shows how something changes in time, and a snapshot of it at one particular...
  9. I

    Solving Schrodinger Equation for Finite Potential Barrier

    Homework Statement I am trying to find the coefficients in a Schrodinger equation approaching a finite potential. https://www.physicsforums.com/showthread.php?t=203385 It is a problem similar to this, except a little easier. In my case, though, there is no V1 as shown in the picture at the...
  10. M

    Schrodinger Equation Explained - Get the Answer Now

    Hey guys, I am trying to understand where did this equation exactly come from. I know it is very complex, but anyone can explain it to me in the best way possible?
  11. A

    Solutions of the Schrodinger equation for hydrogen

    Homework Statement Consider an electron in the hydrogen atom with radial wave function R_{31} (n=3, l=1). Please verify that this radial function verifies the radial equation. Homework Equations The radial equation \frac{1}{r^{2}}\frac{d}{dr}\left(r^{2}\frac{dR}{dr}\right) +...
  12. N

    Continuity equation for Schrodinger equation with minimal coupling

    The Schrodinger equation with the minimal coupling to the Electromagnetic field, in the Coulomb gauge \nabla \cdot A , has a continuity equation \partial_t \rho = \nabla \cdot j where j \propto Re[p^* D p] (D is the covariant gradient D= \nabla + iA . My question is: is there any...
  13. 6

    Solving Schrodinger equation in two dimensions

    Homework Statement Solve the time independent Schrodinger equation for an electron in a 2-D potential well having dimensions Lx and Ly in the x and y directions respectively.Homework Equations d^2Y/dx^2 + d^2Y/dy^2 + 2m/h^2*EY = 0The Attempt at a Solution Y(x) = A exp(jkx) + B exp(-jkx) I'm...
  14. G

    Solving Schrodinger Equation in Two Dimension, r and theta

    Homework Statement It's a two-part problem, the first part was deriving a Schrodinger equation from when x = r cos(theta) and y = r sin(theta) I got: -\frac{\hbar^2}{2m}[\frac{\partial^2}{\partial...
  15. S

    Energy quantization in schrodinger equation

    in schrodinger equation(time independent) d^2y/dx2= 2m/h^2(V-E)y, V is a function of position coordinate, y is eigenfunction. if E>V , y being -ve or +ve it would be a oscillatory function. The allowed energy values are continously distributed...
  16. H

    Varying mass in Schrodinger Equation

    hi, today i learned that if the mass in schrodinger equation is not a constant, then schrodinger equation is not valid. Is there any reason why is it so? Also, what is the different of the time dependent mass m(t) and let say a time dependent angular frequency \omega(t) in a harmonic...
  17. N

    Schrodinger equation problem : part 2

    Homework Statement b)Use the equations a_{-}|\varphi_0\rangle=0 \implies \left(\left(\frac{k}{2}\right)^{1/2}x-\left(\frac{1}{2k/(2m)^(1/2)}\right)^{1/2}\frac{d}{d x}\right)\varphi_0(x)=0 and a_{+}|\varphi_0\rangle=0 \implies...
  18. N

    How Is the Ground State Wave Function for a 1-D SHM Oscillator Determined?

    Homework Statement the ground state wave function for 1-d SHM oscillator is fixed by the diff. eqn a*phi-0=0using the expression for the lower operator as a differential operator,a-=(K/2)1/2x-h*(\partial)/(2pi*(2m)1/2), to find a solution for this differential equation for phi0(x)...
  19. O

    Schrodinger Eqn: Simple Harmonic Oscillator

    Hi, is this the time independent schrodinger equation for a simple harmonic oscillator? -\frac{1}{2}\frac{d^{2}\psi}{dx^2}+\frac{1}{2}x^{2}\psi(x)=\epsilon\psi(x) where epsilon is the rescaled energy eigenvalue.
  20. A

    Solving Schrödinger Eq. for Harmonic Oscillator

    Homework Statement I wonder if someone could help me to arrive at equation 2.56 by performing the substitutions. Please see the attachment Homework Equations Please see the attachment for this part. and also for the attempt of a solution.
  21. LeonhardEuler

    How does the Schrödinger equation lead to the QM theory of measurement?

    Hi everyone, I've recently been bugged by a question I can't seem to find a reasonable answer to. It's about an apparent contradiction between how the wave equation is supposed to evolve in time according to the schrodinger equation and the measurement formalism in QM. Suppose I have any...
  22. V

    Help needed with solutions to schrodinger equation

    Homework Statement hey I am vaibhav,16 an 12th grade..just for pastime i tried to solve schrodinger equation in the 1D 2D 3D spaces. i got the 1D solution(not quantum oscillator), i separated in 2D by polar coordinates but there is a problem in the radial equation as for 3D i know that the...
  23. V

    Solutions to schrodinger equation

    Homework Statement hey I am vaibhav,16 an 12th grade..just as pastime i tried to solve schrodinger equation in the 1D 2D 3D spaces. i got the 1D solution(not quantum oscillator), i separated in 2D by polar coordinates but there is a problem in the radial equation as for 3D i know that the...
  24. A

    Solving the Schrödinger Equation: Need Help!

    Homework Statement Hey guys. I have this problem: http://img32.imageshack.us/img32/1561/78854429.jpg For the first part, I believe that adding those solution is just like adding the two levels of energy they represents and that's way this is not a solution for the equation, I...
  25. C

    Time-dependent Schrodinger equation problem

    Homework Statement For a harmonic oscillator in a state such that a measurement of energy would give either 1/2\hbar\omega or 3/2\hbar\omega with equal probabily. Write the wavefunction solution to the time-dependent Schrodinger equation. 2. The attempt at a solution Given those...
  26. T

    Schrodinger equation of a free particle in the rectilinear

    Schrodinger equation of a free particle in the rectilinear With the wave function in the laboratory reference already known, relate the wave functions of the initial and new references via phase factors, and represent the time and spatial derivatives of the initial wave function with those...
  27. J

    Time indep schrodinger equation

    Homework Statement Show by direct substitution into the time-independent Schrodinger equation that such a particle could be described by the state function Ψ(x) = Ψ_0exp(-ax^2) with a, Ψ_0 constants Homework Equations V(x) = (1/2)kx^2 time independant equation: The Attempt...
  28. R

    Stationary schrodinger equation (basic problems regarding the basis being used)

    i can't seem to understand something very basic about the stationary equation (a "simple" eigenvalue problem): H|Y>=E|Y> H - hamiltonian operator Y - an eigenstate or an eigenfunction of the hamiltonian E - the eigenvalue of the eigenstate as far as i understand, the hamilotian...
  29. K

    Time Dependent Schrodinger Equation -> T(t) solution

    Could someone guide me step by step from the free SE to T(t)=e^(iE_n t)/\hbar ? I am not really familiar with PDEs of any kind and I would like slow step by step analysis! I am just confused by the great many ways of getting from there to there I find in books and Internet, so I would like...
  30. P

    Time Independent Schrodinger Equation Question

    [b]1. State the one dimensional time - INdependant Schrodinger equation for a particle of mass m and total energy E in a potential V(x). For an infinite square potential well V(x)=0 (0<x<l) and V(x) = infinite (all other x) find a general solutionfor the wavefunction of this function of this...
  31. P

    Schrodinger equation reduction using substitution

    SOLVED: Schrodinger equation reduction using substitution Homework Statement Given \frac{d^2 \psi}{dx^2} - Ax\psi + B\psi = 0 make a substitution using w= A^{1/3} (x - \frac{B}{A}) to get \frac{d^2 \psi}{dw^2} - w\psi = 0 Homework Equations The Attempt at a Solution...
  32. H

    Discrete Analog of Schrodinger Equation?

    It seems like there should be a discrete-time discrete-space analog to the Schrodinger equation. For example, you can apply the classic explicit finite difference method to the heat equation and get a simple binomial or trinomial tree relationship in a lattice. When I try that with the...
  33. F

    Schrodinger Equation and wavefunction collapse

    If we solve the Schrodinger Equation for hydrogen atom, we get discrete energy levels that agree with experiment. But no where we need the wave function collapse. So my question is where the wave function come from and why do we need it?
  34. E

    Schrodinger Equation for a central 2D potential

    Hello, I would like to ask something about central potentials. When I am working in 3D, I haven´t got any problem solving the schrodinger equation since I use the following change of variables: -\frac{\hbar^{2}}{2m}\nabla^{2}\Psi+V(r)\Psi=E\Psi \Psi=\frac{\chi}{r} With this change of...
  35. G

    Time-Dependent Schrodinger Equation

    Homework Statement Verify that for the wave function |\Psi| = a2|\Psi21| + B2|\Psi22| + 2aB\Psi1\Psi2cos(w21t) all psis are really psi(x) and the left side of the equation is pis(x,t) Homework Equations a B psi's are all real The Attempt at a Solution We are not sure about...
  36. W

    Numerially integrate the radial schrodinger equation

    i now need to integrate the time-dependent schrodinger equation in 2D the potential is rotationally invariant and so is the initial wave function thus the symmetry of the initial wave function will be preserved in time Instead of a 2D equation, i now only need to integrate a 1d equation...
  37. K

    Schrodinger equation and free particles

    Homework Statement Show whether the functions psi_I = A cos(kx - wt) psi_II = A sin(kx - wt) are solutions of Schrodinger equation for a free particleHomework Equations Schrodinger equation The Attempt at a Solution For psi_I = A cos(kx - wt), d2psi_I/dx2 = -Ak2psi[/SUB]I[/SUB] dpsi_I/dt =...
  38. K

    Partial Differentiation in free Schrodinger Equation

    Hello again! This time I have another calculus question for you, coming straight out of my study of the free Schrodinger equation, since I am not that experienced with that kind of derivative. It all starts with a given wavefunction (which I think is 2-dimensional,correct me if wrong)...
  39. E

    Schrodinger equation from commuation relations

    I was wondering- is it possible to derive an equation of motion for example, the Schrodinger equation from the uncertainty principle (in commutator form)? i.e. Is it possible to derive the Schrodinger equation from the following: \left[\hat{x},\hat{p}\right]=ih I gave it a shot, but of...
  40. B

    Classification of schrodinger equation?

    the schrodinger equation is sometimes called a wave equation and in my quantum mechanics text's they often show the wave equation comparing it to the schrodinger equation. i don't understand why they do this when it is of the same form as the heat equation, it's not second order in time like the...
  41. D

    What is the Schrodinger Equation?

    So I've been looking online @ Schrodinger's Equation, but I still can't get a good grasp of what it's all about... All I know so far is that its part of quantum mechanics and that its solutions describe atomic and subatomic systems, electrons and atoms.. <---but what does that actually mean...
  42. A

    Solving using schrodinger equation techniques

    Hello, I have problem I wish to solve, and I wonder if anyone already delt with it when solving the schrodinger 2D equation. say E(x,y) is a scalar field function that complies with ( \frac{d}{dx}2+\frac{d}{dy}2 ) *E(x,y)+k(x,y)*E(x,y)=k1*E(x,y) where k(x,y)={k2 for x2+y2<R2 and 0...
  43. B

    Proving solutions to the schrodinger equation

    Homework Statement Verify that the following are not solutions to the Schrodinger equation for a free particle: (a) \Psi(x,t) = A*Cos(kx-\omega t) (b) \Psi(x,t) = A*Sin(kx-\omega t) Homework Equations Schrodinger equation: \frac{-hbar^2}{2m}\frac{\partial^2\Psi}{\partial x^2} =...
  44. R

    Solving the Schrödinger equation for hydrogen atom

    Homework Statement Hello. I'd like to solve this: -\frac{\hbar^2}{2m}\nabla^2 \Psi(r,\theta,\phi) -U(r) \Psi(r,\theta,\phi) = E\Psi(r,\theta,\phi) Homework Equations The Attempt at a Solution I can separate the variables, but that's about it. \frac{1}{R(r)}...
  45. T

    What's wrong with my Schrodinger equation?

    Hi everyone, I'm having an issue trying to make the abstract form of the schrodinger equation: i\hbar\frac{\partial}{\partial t}\left|\psi\right\rangle = H\left|\psi\right\rangle be consistent with the form that operates on wavefunctions in the position representation...
  46. K

    Solving Potential V with Schrodinger Equation

    Assume the potential in question is V = \left\{ \begin{matrix} \infty, \qquad x<0 \\ -V_0, \qquad 0\leq x \leq a \\ 0, \qquad x>a \end{matrix} \right. where V_0 is positive. if we need to find the bound state, we consider the energy is less than the potential. But the...
  47. M

    Solving Schrödinger Equation: A, V(x), and a Hint

    Homework Statement Please see attached image . Homework Equations Schrödinger Equation The Attempt at a Solution For part a ) |\psi|^{2} = A For Part b) V(x) = 0 For Part c) Just need a hint
  48. M

    Solving the Schrödinger Equation

    Homework Statement Please see attached image . Homework Equations Schrödinger Equation The Attempt at a Solution For part a ) |\psi|^{2} = A For Part b) V(x) = 0 For Part c) Just need a hint
  49. S

    Solving the schrodinger equation

    Homework Statement i want to find a pure geometric interpretation of wave function in quantum mechanics Homework Equations i want to solve schrodinger's equation as a second order partial differential equation with a pure mathmatic way to find its geometric analogous The...
  50. K

    What is the General Solution for the Schrödinger Equation in a 2D or 3D Box?

    The solution of the one dimensional Schrödinger equation for a particle in a one dimensional box is Asin \frac{n \pi x}{a}. But how about if the box is 2D or 3D?
Back
Top