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. PsychonautQQ

    Infinite Well with Schrodinger equation

    Homework Statement I'm having a bit of trouble following my textbook, I was under the impression ψ(x) = e^i(kx) = Cos(kx) + iSin(kx) but in my textbook they write the general solution to this equation as ψ(x) = ASin(kx) + BCos(kx). How come they wrote the sin part as not imaginary? isn't this...
  2. W

    Integrating the time-indepdent Schrodinger equation

    Homework Statement A particle of mass m is confined to move in a one-dimensional and Diract delta-function attractive potential V(x)=-\frac{\hbar^2}{m}\alpha\delta(x) where \alpha is positive. Integrate eh time-independent Schrodinger equation between -\epsilon and \epsilon. Let...
  3. C

    How to gain an understanding of the Schrodinger equation for a noob

    Should I start by learning about the equations for classical harmonic waves and how the de Brolier equations can be applied to them? What else should I learn? I'm a chemistry student and we did a class on quantum chemistry, but the mathematical side of it was way too complicated for me so I just...
  4. G

    Is the Non-relativistic Schrodinger Equation the right one?

    Okay, so I'm actually an economics major but I LOVE physics; especially quantum physics. Unfortunately my knowledge of physics is limited only to the conceptual side of physics (something I'm working on changing). I spent a lot of time thinking of getting a tattoo I really wanted and settled on...
  5. C

    Separate variables schrodinger equation

    Homework Statement [2 Dimensional infinite square well] Show that you can separate variables such that the solution to the time independent schrodinger equation, ## \hat{H} \psi (x,y) = E \psi (x,y) ## can be written as a product state ## \psi (x,y) = \phi (x) \chi (y) ## where ## \phi (x)##...
  6. A

    Schrodinger equation subjected to general potential

    There are few questions on an assignment (taken from an old exam, YIKES!) that are confounding me and I was wondering if you in the physics community could help. Here is the question; Given the wavefunction, ψ(x,t)=∫PHI(p)*exp[i((px-E(p)t)/hbar)]dp For the case where a quantum particle is...
  7. A

    Changing variables in the Schrodinger equation

    Suppose I have a Schrodinger equation for two interacting particles located at x and y; so, something like \left( i \frac{\partial}{\partial t} + \frac{1}{2m_x} \frac{\partial^2}{\partial x^2} + \frac{1}{2m_y} \frac{\partial^2}{\partial y^2} + V(x-y) \right) \psi(x,y,t) = 0. Now, I want to...
  8. C

    Schrodinger equation, potential energy function

    A particle of mass m is in the state \Psi (x,t) = A e^{-a[(mx^2 / \hbar ) + it]}Find A For what potential energy function V(x) does \Psi satisfy the Schrodinger equation? Do I just re-arrange for A? (Sorry if I seem really dumb). I'm not really getting this.
  9. M

    Dark state & schrödinger equation

    Hello, this is my first thread here and i have a question regarding coherent population trapping and the dark state. I am from Germany, so please excuse me, when my english isn't very good. This is what I found on wikipedia: http://en.wikipedia.org/wiki/Dark_state in the section...
  10. W

    What is the use of WKB after Schrodinger equation is established?

    i think every system is accurately described by Schrodinger equation. so what is the point of using old quantum mechanics methods? with Schrodinger equation, at least numerically, you can solve the eigenvalues and eigenvectors readily and accurately. So what is the point of using...
  11. B

    Schrodinger equation for close and opens system

    How do we differentiate the solution of Schrodinger equation for closed and open system.
  12. F

    Two-dimensional Schrodinger equation

    Homework Statement An ice-hockey puck has the weight 0.170 kg. The ice-hockey rink is 30x60 m. If no players are on the ice, what speed does the puck have due to the quantum effects (ground state)? Homework Equations The wave-equation solution to the Schrodinger equation is ψ(x,y) =...
  13. W

    How to normalize Schrodinger equation

    Homework Statement The solution to the Schrodinger equation for a particular potential is psi = 0 for absolute x > a and psi = Asin(pi*x/a) for -a <= x <= a, where A and a are constants. In terms of a, what value of A is required to normalize psi? Homework Equations psi = 0 for absolute...
  14. tsuwal

    Solve Schrodinger equation for an eletron in a box. Why discrete?

    Homework Statement An eletron is moving along one axis between x=0 and x=L. It's mass is given by m. We want to know the energy and wave function of its possible states given by the quantic number n. Show that the solution to the above equation is En=n^2*h^2/(8*m*L^2)...
  15. tsuwal

    Schrodinger equation dedution step?

    My chemistry teacher showed this slide but didn't explained how the marked step in the dedution of the schrodinger equation. Please help! I really don't know where I can find the answer, it's the first time I see the Schrodinger equation!
  16. A

    Can someone give me some examples on the schrodinger equation?

    So I understand the schrodinger equation (independent), but I'm a kind of person who understands something better after an example or two, can someone help me and give me one for a H-atom or Hormonic Oscillator? Thanks, and sorry if this is the wrong place to put this post...
  17. ShayanJ

    Exploring Non-Separable Solutions for the Time-Dependent Schrödinger Equation

    Everywhere I look,in every textbook,online texts,video tutorials,everywhere,Schrödinger equation is always solved via separating variables. I want to know is there a way to solve Schrödinger equation(of course I mean time-dependent Schrödinger equation)without separating variables? Is it...
  18. S

    Schrodinger equation in two dimension

    Hi everybody! I would kindly ask you if somebody know some method to solve analitically the following equation (written in cylindrical coordinates): \Big[\frac{\partial^2}{\partial\rho^2}+ \frac{1}{\rho}\frac{\partial}{\partial\rho}+\frac{\partial^2}{\partial...
  19. C

    Solution to the Schrodinger equation

    I know that one solution to the Schrodinger equation is Aexp(i(kx - ωt)) Is there a special relationship between k and ω for this to be a solution, or is it always a solution?
  20. Z

    Time independent Schrödinger equation

    Should the time independent Schrödinger equation contain a differentiating 'd' as shown here: http://vergil.chemistry.gatech.edu/notes/quantrev/node8.html or a differentiating curly 'δ' as shown here: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/scheq.html Thank you!
  21. A

    Schrodinger equation help

    Homework Statement What is the probability that a particle in the ground state will be found between L/2 and 2L/3? im new guys so go easy :) Homework Equations ∫ψ(x)^2 dx = ∫2/L (sin(πx/L))^2 dx in attachment The Attempt at a Solution The answer should be 30.44% i got 66.66% and sometimes a...
  22. L

    Problems in simulating Time Dependent Schrodinger Equation

    I'm trying to simulate wavepacket propagation in various potentials (so far in 1D). I'm writing in C++, and using allegro graphics library. The TDSE is: \frac{∂ψ}{∂t} = \frac{i \hbar}{2m} \frac{∂^2 ψ}{∂ x^2} - \frac{iV}{\hbar}ψ So what I've done was writing out the real and imaginary parts...
  23. P

    Question about Schrödinger equation interpretation

    Homework Statement Im reading and thinking about the interpretation about Schrödinger equation s solutions (wave functions) - what they really mean. What does the amplitude of wave function correspond to? Does it mean that if amplitude is greater then energy of particle is greater as well ...
  24. dbmorpher

    What is the schrodinger equation?

    I have seen its name in many articles I have read but I would like to know. What is it and what is its use?
  25. M

    Schrödinger Eq: Neglect Uncertainty Principle? Intensity Probability?

    Does the Schrödinger equation completely neglect the uncertainty principle? If so, wouldn't this imply that our intensity distribution has its own probability distribution?
  26. A

    Negative energy in the Schrödinger equation

    When my book deals with bound states and scattering states it puts: E<0 bound state, E>0 scattering state. What reference for the potential have been used for these?
  27. A

    Potential in the schrödinger equation

    In clssical mechanics it doesn't really seem to matter which reference point you use for your potential. All that matters is the difference in potential between two points. Does the same hold true for the potential you plug into the Schrödinger equation? It doesn't seem so since plugging in...
  28. A

    Change of Schrodinger equation when we change frame of reference

    Hi! I think this should be a fairly easy question to resolve, but it's currently giving me fits... Suppose we consider a system of three interacting particles where we assume two of the particle (at positions r1 and r2) have infinite mass (such that we can ignore their kinetic energy) and do...
  29. Q

    Showing that the Schrödinger equation implies the de Broglie relation when PE=0

    Hello, In the book physical chemistry (P. Atkins & Julio de Paula, 2009, 5 ED) the authors derive a justification of the Schrödinger equation. 1.) \frac{-\hbar^{2}}{2m} \frac{d^{2}\psi}{dx^{2}}+V(x)\psi=E \psi The derivation goes as follows: Derivation: We can justify the form of...
  30. D

    Schrodinger equation, lowest potential energy

    Classically, particles seek configurations of least potential energy. Something like this happens in QM: the wavefunction will usually be densest in those areas the potential energy is smallest. But looking at the Schrodinger equation itself, I can't see intuitively why this should be.
  31. C

    Greens Function Solution of Schrodinger Equation

    Homework Statement Using the Greens function technique, reduce the Schrodinger Equation for the following potential: V = V0 , 0<x<a V = infinite, elsewhere. Homework Equations The Attempt at a Solution I have no idea what "reduce" means. The professor did not go over this...
  32. A

    What kind of differential equation is the Schrodinger equation?

    Does it have an easy classification (elliptic, hyperbolic, parabolic, for example)? Or does the fact that it has an "i" in it make this impossible?
  33. B

    Rigid Box and 3D Schrodinger equation

    Homework Statement An electron is confined within a three-dimentional cubic region the size of an atom where L = 200 pm. a) write a wave equation for the electron b) wirte a general wave function for the possbile states of the electorn. List any quantum numbers and their possible values...
  34. B

    Schrodinger equation for three dimention?

    I have learned time-independent schrodinger equation only from my textbook. I know Eψ(x) = - hbar^2 / 2m ψ''(x) + Uψ(x) and ψ(x) = Asinkx + B coskx what if it's three dimention? do I do Eψ(x, y, z) = - hbar^2 / 2m ψ''(x, y, z) + Uψ(x, y, z) ? and what is the wave equation supposed to be?
  35. B

    1 Dimentional Schrodinger equation

    Homework Statement Consider the one dimensional wave funciton give below. a) Draw a graph of the wave function for the region defined. b) Determine the value of the normalization constant c) what is the probability of finding the particle between x = 0 and x = a/2 d) show that the wave function...
  36. T

    Two level system Schrodinger Equation problem

    Hello guys, in the attached file, I can't understand how the guy arrived to the equation in the red rectangle. My problem is: how could there not be dC2/dt term. Why only dC1/dt term? ψ contains both C1 and C2, and when the derivative is applied, both have to be influenced, and both are...
  37. N

    Explanation of a failed approach to relativize Schrodinger equation

    I'm reading the Wikipedia page for the Dirac equation I am not sure how one gets a new \rho and J^\mu. How does one do to derive these two? And can anyone show me why the expression for density not positive definite?
  38. P

    Using symmetry solving Schrödinger equation

    Homework Statement When solving, say, the double delta function potential well, we fix constants using continuity. If the potential is symmetrical about the origin, can we conclude that the wave function, i.e. the solution, will also be symmetric? I found this way made the calculations much...
  39. S

    Does the Schrodinger Equation Describe Particles Popping In/Out of Existence?

    Hello - A few questions I have after watching Brian Green’s The Elegant Universe – Within the video Dr. Green shows a neat way to view the different scales relativity and quantum mechanics are involved with. He takes an elevator to a top floor to show relativity’s applicable scale. He steps...
  40. Jonnyb42

    Schrodinger Equation, Potential

    Schrodinger Equation, "Potential" This is a very simple question, but I am confused. I have seen Potential and Potential Energy interchanged.. yet still referred to as potential. Is the "potential" function in the schrodinger equation really a potential function or potential energy? (units...
  41. I

    How does a non-linear Schrodinger equation implies non-unitary evolution?

    Hi, I several times heard that one way to describe the collapse of the wave-function is to add non linearities in the Schrodinger equation (I know that this approaches are not convincing but that's not my point), however, I don't see why a non linear SE would imply loss of unitarity? As long...
  42. 9

    Help with the Schrödinger Equation.

    So I've been trying to understand this equation for a long time, about half a year - I don't know someone who could teach me this either due to the fact that I am only 15 and going into my final year in secondary school after August and according to most colleges (UK college, not American) in my...
  43. W

    About Green's function in time dependent schrodinger equation

    While I was studying Ch 2.5 of Sakurai, I have a question about Green's function in time dependent schrodinger equation. (Specifically, page 110~111 are relevant to my question) Eq (2.5.7) and Eq (2.5.12) of Sakurai say \psi(x'',t) = \int d^3x' K(x'',t;x',t_0)\psi(x',t_0) and...
  44. A

    TIme-independent schrodinger equation

    I've been looking into the time independent schrodinger equation (E\Psi = Ĥ\Psi.) I know that \Psi is the wave function and Ĥ is the hamiltonian operator. I know that Ĥ is the total of all the energies in a system. What exactly is the wave function? Is it a quantum state? And what does the E...
  45. A

    Time-dependent Schrodinger equation for many particles

    If you've got, say, three particles, then the time-dependent Schrodinger equation (in units where \hbar = 1) for the system reads i \frac{\partial \psi}{\partial t} = -\sum_{i=1}^3 \frac{1}{2m_i} \Delta_i \psi + \sum_{i<j} V(r_i - r_j)\psi, right? And of course \psi = \psi(r_1,r_2,r_3;t)...
  46. M

    Schrodinger Equation and seperation of variables

    Hi, In Griffiths QM, it is claimed that to solve the Schrodinger Equation, we take the solution wavefunction \Psi(x,t) to be of a seperable form \psi(x)\phi(t). He then says that a superposition of these seperable forms can always give us the general solution. Can someone help me prove that...
  47. L

    Understanding schrodinger equation

    Note : I am not sure this is the right section for posting it , but from the rules section i saw that this section can be used for homework related queries and independent study . Homework Statement Understanding schrodinger equation . i want to understand the solutions of this equation and...
  48. Y

    Schrodinger Equation in a representation

    The general evolution of a ket |\psi\rangle is according to -i\hbar\frac{d}{dt}|\psi\rangle=H|\psi\rangle without specifying a representation. From this equation, how can you simply get a equation in a certain representation F as below: -i\hbar\frac{\partial}{\partial t}\langle...
  49. N

    The Schrödinger equation as the non-relativistic limit of the Dirac equation

    Hello, I'm reading Griffiths' introduction to elementary particles and he seems to claim that the Schrödinger equation can be seen as a non-relativistic limit of the Dirac equation. I was wondering how one could deduce this, e.g. how do we go from \mathcal L = \bar{\psi} \left( i \gamma^\mu...
  50. 3

    Question about Schrodinger equation

    Ok, I understand the schrodinger equation for the most part, the thing is though, I don't understand what ∂ means... In the equation:(∂^2ψ/∂x^2)+8(pi)m/h^2(E-V)ψ=0 It pops up two times. The rest of the equation is kinda self explanatory, but I don't know what on Earth ∂ means please, tell me...
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