What is Schrödinger: Definition and 611 Discussions

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. 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...
  2. M

    Solving 3D Schrodinger Equation - Explaining 1/X(x) Term

    The schrodinger equation in 3D (time independent). Letting Phi = X(x).Y(y).Z(z), and solving as a PDE... The equation looks pretty much the same except there is a separate Hamiltonian for each of the Cartesian coordinates x y z. However, the 1/X(x) term etc. really confuses me, I don't...
  3. 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 =...
  4. I

    How do I effectively normalise the Schrodinger PDF with given conditions?

    Homework Statement Normalise \Psi(x,t) = Ae^{-\lambda |x|}e^{-i \omega t} Homework Equations (i.e. it must satisfy \int_{-\infty}^{\infty} |\Psi (x,t)|^2 dx=1) The Attempt at a Solution This is my first attempt at normalisation and I don't know how valid my reasoning is, can...
  5. 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...
  6. 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...
  7. 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?
  8. 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) +...
  9. 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...
  10. 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...
  11. 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...
  12. 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...
  13. haushofer

    Quick question on the Schrodinger symmetry group

    Hi, I'm reading the article "Galilean Conformal Algebra's and AdS/CFT", 0902.1385v2, and have a quick question about the Schrodinger symmetry group. The symmetry group consists of the usual Galilean group G(d,1) with rotations, boosts and (space and time) translations. On top of that we have...
  14. R

    Hermitian operators in schrodinger eqn.

    If the Hamiltonian is given by H(x,p)=p^2+p then is it Hermitian? I'm guessing it's not, because quantum-mechanically this leads to: H=-h^2 \frac{d^2}{dx^2}-ih\frac{d}{dx} and this operator is not Hermitian (indeed, for the Sturm-Liouville operator O=p(x)\frac{d^2}{dx^2}+k(x)\frac{d}{dx}+q(x)...
  15. 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...
  16. 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...
  17. 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)...
  18. 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.
  19. 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.
  20. 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...
  21. A

    What makes schrodinger cat quantum?

    Hi I am learning quantum physics in 2nd year i want to know what makes Schrodinger cat quantum? how do we ended up in the Copenhagen interpretation? i.e. probability density function = 0.1; 0<x<10; =0 everywhere else we could say that the particle is simply moving very fast (ignoring...
  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. E

    Schrodinger Equations and Probability Density Functions

    Homework Statement A Particle is described by the normalized wave function psi(x,y,z) = Ae^(-alpha[x^2 + y^2 + z^2]) Where A and alpha are real positive constants a)Determine the probability of finding the particle at a distance between r and r+dr from the origin hint: use the volume of...
  27. 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...
  28. 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...
  29. 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...
  30. K

    Schrodinger Equations - wave propagation

    Hi, Can somebody point me in the correct direction of learning about Schrodinger Equations in relation to Wave propagation. I came across Schrodinger Equations in some texts but couldn't quite understand some background. Most of the time the author used it from nowhere. Really appreciate if...
  31. 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...
  32. D

    Relation between (simplified) elastic d. eqn. and classical schrodinger eqn?

    Hello, Homework Statement I wondered if someone could help me show / give hints on how to show the (simplified) elastic differential equation (below) is related to the classical Schrodinger equation (in quantum mechanics)? I am a maths undergraduate. 2. Homework Equations - (i had some...
  33. 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...
  34. 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...
  35. 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...
  36. S

    When can the time-independent Schrodinger be used?

    Hi, I am new to this forum. I realized that I was browsing the forums way too much and I said why not register and post some questions that have been lingering in my head: Here is one: In a periodic solid, we almost always neglect the time factor of the Schrodinger equation: e^{-i...
  37. 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?
  38. 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...
  39. 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...
  40. 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...
  41. 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 =...
  42. 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)...
  43. 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...
  44. 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...
  45. S

    Normalisation of Schrodinger Eq.

    Homework Statement Suppose you assume that you have normalised a wave function at t = 0. How do you know that it will stay normalised as time goes on? Show explicitly that the Schrodinger equation has the property that it preserves normalistion over time. Homework Equations From my notes I...
  46. 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...
  47. 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...
  48. 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} =...
  49. 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)}...
  50. 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...
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