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.

View More On Wikipedia.org
  1. Danielk010

    What is the energy equation in Schrodinger's Spherical equation?

    I attempted the problem by first finding the radial, theta, and phi equation for the ground state of a hydrogen atom. I multiplied the three equations to get the wave equation. From there, I took each derivative in the Schrodinger Spherical equation and found that ## \frac {\partial^2 \psi}...
  2. Marioweee

    Creating Schrödinger cat states with trapped ions

    I have already solved question number 1 by applying the schrödinger equation obtaining that $$\ket{\psi_2}(t) = \cos(\Omega t)\ket{g} - i \sin (\Omega t)\ket{s}$$ and therefore in ##t=\frac{\pi}{4\Omega}## $$\ket{\psi_2}(t) = \dfrac{1}{\sqrt{2}}(\ket{g} - i \ket{s})$$ I have some doubts...
  3. S

    I Does Schrodinger's Cat contradict itself?

    In the schrodinger's cat thought experiment is the cat technically the observer because The cat can observe if its alive or dyeing? Should schrodinger's thought experiment only work with non living objects?
  4. hilbert2

    A Ground state calculation with a time averaged wave function

    An idea I was thinking about for the last few days: You want to calculate the ground state of some system from the Schrödinger eqn ##\hat{H}\left|\psi\right.\rangle = E\left|\psi\right.\rangle##. One way is to choose a trial state ##\left|\psi (t_0 )\right.\rangle## and use the TDSE to...
  5. snoopies622

    I How to add time variation to a Schrodinger operator?

    I'm looking at Dirac's "Lectures on Quantum Field Theory" and I have a question about the basic mathematics of something that's part of ordinary quantum mechanics. On page 3, he says, The two pictures are connected in this way: any Schrodinger dynamical variable is connected with the...
  6. A

    A Schrodinger equation in quantum field theory

    What is the Schrodinger equation in QFT? is it the nonrelativistic approximation of a Klein-Gordon scalar field? or Is there more? I have read that the Schrodinger equation describes a QFT in 0 dimensions. I accept every answer
  7. L

    I Time-dependent to time-independent Schrödinger equation

    Why you can do separation of variables in time-dependent Schrödinger equation i \hbar \frac{\partial \psi(\vec{r},t)}{\partial t}=-\frac{\hbar^2}{2m}\Delta \psi(\vec{r},t)+V(\vec{r})\psi(\vec{r},t) with \psi(\vec{r},t)=\varphi(\vec{r})T(t) and when in general is that possible?
  8. Que7i

    Schrödinger Equation (why are U and -x^2 =0?)

    I've already found out how to do it, but, either I got lucky and my procedure is wrong or I just don't get it. Why are U and -x^2 equal 0?
  9. Samama Fahim

    I Schrodinger Equation from Ritz Variational Method

    (This is from W. Greiner Quantum Mechanics, p. 293 from the topic of Ritz Variational Method) 1) Are ##\frac{\delta}{\delta \psi^{*}}## derivatives in equations 11.35a and 11.35b? If this is so, we can differentiate under the integral sign to get ##\int d^3x (\hat{H}\psi)## in equation 11.35a...
  10. D

    A practice problem with Schrodinger equation

    So my question is.. Is schrodinger equation for this problem like this?: How to use the condition that E=0? Thank you
  11. E

    Proof of Schrodinger equation solution persisting in time

    I've started reading Introduction to Quantum Mechanics by Griffiths and I encountered this proof that once normalized the solution of Schrodinger equation will always be normalized in future: And I am not 100% convinced to this proof. In 1.26 he states that ##\Psi^{*} \frac{\partial...
  12. gentzen

    A Dieter Zeh's MWI as Schrödinger equation + further assumptions

    Sorry for derailing that discussion even further. My reference to Dieter Zeh's German book was unlucky, not just because it is not a peer reviewed paper, but also because I did not remember the exact place with the remark. Since this has bothered me since a long time anyway, I now searched the...
  13. K

    I Schrodinger equation for N particles in a box

    [Pathria, statistical mechanics][1], pg2 ,when discussing ##N## particles in a volume ##V## "...there will be a large number of different ways in which the total energy E of the system can be distributed among the N particles constituting it. Each of these (different) ways specifies a...
  14. ThiagoSantos

    I Wave function using the time dependent Schrodinger equation

    Given a wavefunction ψ(x, 0) of a free particle at initial time t=0, I need to write the general expression of the function at time t. I used a Fourier transform of ψ(x, t) in terms of ψ(p, t), but, i don't understand how to use green's functions and the time dependent schrodinger equation to...
  15. Hamiltonian

    I Derivation of Schrodinger equation (chicken and egg problem?)

    The classical wave equation in 1-D reads: $$\frac{\partial^2 u}{\partial x^2}(x,t) = \frac{1}{v^2}\frac{\partial^2 u}{\partial t^2}(x,t)$$ The D'alembert solution to the wave equation is: $$u(x,t) = f(x+vt) + g(x-vt)$$ so a allowed wave function solution to the 1-Dimensional classical wave...
  16. Hamiltonian

    I Using the Schrodinger eqn in finding the momentum operator

    I have read that the Schrodinger equation has no formal derivation we are simply applying the Hamiltonian operator on the wave function $$\hat H = i\hbar \frac{\partial}{\partial t} = \hat T + \hat V$$ here we substitute $$\hat T = \frac{\hat p^2}{2m}$$ where $$\hat p = -i \hbar...
  17. Killtech

    A Schrödinger's original interpretation

    I wasn't sure if i should call it an "interpretation" and post it in this forum or not as it isn't entirely clear if it makes any different predictions within its region of it validity. Anyhow, the original idea of Schrödinger that made him come up with his equations is very different from the...
  18. Wannabe Physicist

    Exploring the Time-Energy Uncertainty Relation to Solve a Schrodinger Equation

    I am guessing time-energy uncertainty relation is the way to solve this. I solved the Schrodinger equation for both the regions and used to continuity at ##x=-a, 0,a## and got ##\psi(-a<x<0) = A\sin(\kappa(x+a))## and ##\psi(0<x<a) = -A\sin(\kappa(x-a))## where ##\kappa^2 = 2mE/\hbar^2##...
  19. Tymothee Waldner

    I Schrödinger wave function: How to use it to get 3-D atomic orbitals?

    Hi, I am 16 year old and I am very interested in Physics. This summer I solved Schrödinger equation using griffiths' introduction to quantum physics and other sources. I achieved to get an exact solution of the wave function but I would like to plot it in a programm in order to get the 3d...
  20. D

    I Schrodinger Cat states in terms of Displacement Operator

    The coherent state can be written in terms of e^(αb†+α∗b)|0>. But how the even coherent state i.e. |α>+|-α> can be written in terms of displacement operator?
  21. thegroundhog

    I Proving the Schrodinger Equation

    How did scientists prove the accuracy of Schrodinger's equation to describe the behaviour of subatomic particles, especially in the 1920s? How do you monitor an electron's momentum and position when they are so small? Also, if the Schrodinger equation just describes probabilities, is the...
  22. L

    I Schrodinger Equation as Flow Equation

    I was playing with the Schrodinger equation and realized that it can be interpreted as a flow equation. If we set $$ \psi = A e^{i \theta} $$ We can put the Schrodinger in the form ∂ψ∂t=(−∇ψ)⋅v+iEψ If v=ℏθm and E=ℏ2m(−∇2AA+∇2θ)+ρV I find this intuitive personally as it shows that the...
  23. Wrichik Basu

    I Numerically solving Time-independent Schrödinger eqn. using Shooting algorithm

    I have to solve the 1D Time-independent Schrödinger equation (TISE) using the shooting algorithm. As far as I understood from this video on Shooting method for solving BVP, I will have to solve the problem by using IVP solvers (like RK2 or RK4 methods), and guess a value for the derivative of...
  24. C

    Solving 1-D Schrodinger Equation in Python (Scipy) Numerically

    I've tried to make an animation using python to demonstrate the 1-D simple harmonic oscillator and step potential examples. Hope that it can be useful for some of you. Have fun~ :) https://blog.gwlab.page/solving-1-d-schrodinger-equation-in-python-dcb3518ce454 By the way, If you are...
  25. O

    I General solution of the hydrogen atom Schrödinger equation

    Hello everyone! I have two questions which had bothered me for quite some time. I am sorry if they are rather trivial. The first is about the general solution of the hydrogen atom schrödinger-equation: We learned in our quantum mechanics class that the general solution of every quantum system...
  26. Huzaifa

    Explain the Schrodinger equation

    Please explain in simple words, the meaning of the Schrodinger wave equation in the quantum mechanics model of atom. $$\frac{\partial^{2} \psi}{\partial x^{2}}+\frac{\partial^{2} \psi}{\partial y^{2}}+\frac{\partial^{2} \psi}{\partial z^{2}}+\frac{8 \pi^{2} m}{h^{2}}(E-U) \psi=0$$
  27. Tuca

    I Solving Schrödinger's equation for a hydrogen atom with Euler's method

    Hi, first-time poster here I'm a student at HS-level in DK, who has decided to write my annual large scale assignment on Schrödinger's equation. My teacher has only given us a brief introduction to the equation and has tasked us to solve it numerically with Euler's method for the hydrogen atom...
  28. S

    I Matrix Notation for potential in Schrodinger Equation

    I'm working on the time-dependent Schrodinger equation, and come across something I don't understand regarding notation, which is not specific to TDSE but the Schrodinger formalism in general. Let's say we have a non-trivial potential. There is a stage in the development of the TDSE where we...
  29. fresh_42

    AI meets Chemistry in solving electronic Schrödinger equation

    Abstract: The electronic Schrödinger equation can only be solved analytically for the hydrogen atom, and the numerically exact full configuration-interaction method is exponentially expensive in the number of electrons. Quantum Monte Carlo methods are a possible way out: they scale well for...
  30. S

    How is Information Stored in Quantum Systems?

    Interest in Schrodinger's question ... consciousness and how is information stored within quantum entanglement and coherence ... how do we know what we know. Biological systems are constantly changing interfacial at the boundaries yet retention of information is retained in time even with the...
  31. AndreasC

    I Pros and cons of Heisenberg and Schrodinger (and Feynman) pictures?

    So there's this professor who insists that the Heisenberg picture is all the rage and much superior in most ways to the Schrodinger picture. He compares it to how you don't use the Hamilton-Jacobi formulation of classical mechanics as much as the Hamiltonian one. Alright, I can buy it. I...
  32. E

    Schrodinger Equation Research Question

    Hey guys, I have had my eye on quantum mechanics for a while now and finally decided that I have a large enough understanding of the concept/math/theories behind it to write a research paper on it, specifically Schrodinger Equation. But I am having a hard time finding a good research question...
  33. P

    Particle in a box : Schrodinger Eq

    Hi, I'm trying to prove a wave equation of particle in a box situation. In many solutions, they used a equation like Eq = Asin(kx)+Bcos(kx). Instead, I want to prove using Eq = Aexp(ikx) + Bexp(-ikx). So, this is my solution. However, the original (well-known) solution is without i. (psi =...
  34. LCSphysicist

    Schrodinger equation in three dimensions. Atom with one electron.

    When solving the Schrodinger equation by separation of variables to atom with one electron and in the spherical coordinates, we get $$\Psi = \Theta(\theta)\phi(\varphi)R(r)$$ Specifically, $$\phi = e^{im\rho }$$ The question is, why we adopt this particular solution, in general, we have this...
  35. T

    I How did Schrödinger find his equation?

    So the question is pretty simple, how did he came up with the wave function and why does the Schrödinger eq model / predict the change of the wave function throw time?
  36. Ssnow

    I Schrodinger equation on the complex disk

    Hi to all member of the Physics Forums. I have this question: it is possible consider the analogue of the Schrodinger equation on the plane with configuration space ##(x,p)\in\mathbb{R}^4## on the complex disk ##\mathbb{D}=\{z\in\mathbb{C}: |z|<1\}##? Ssnow
  37. W

    Analytic solution of the SHO for 1D Schrodinger

    At the point where we 'guess' a solution to this 2nd order ODE that cannot be done analytically, I was wondering why Griff and others choose $$e^{-x^2 / 2}$$ rather than just $$e^{-x^2}$$ I've plotted both here and am left wondering what's so different? If we guessed instead the unpopular...
  38. P

    A De Broglie to Schrödinger to Thomson to Bohm?

    I'm investigating some newly conceived Hamiltonians using the approaches of de Broglie and Schrödinger as jumping off points. Lanczos in "The Variational Principles of Mechanics" p. 278 describes and analyzes them. Neither de Broglie nor Schrödinger really completed the program of the H-J...
  39. JorgeM

    Gaussian wavepacket as a solution of the Schrödinger equation

    The Schrödinger equation I need to prove is this one And the Gaussian wavepacket is found here Thanks for your advice. JorgeM <Moderator's note: upload images to PhysicsForums. Do not use external image servers.>
  40. S

    I Did Schrödinger himself take his "Cat Experiment" seriously?

    In 1935, Austrian physicist Erwin Schrödinger was looking at a concept called a "superposition." Superposition is when two waves meet and overlap and interact, which can lead to different results based on the circumstances. The concept can be seen in the regular-sized world as well, in...
  41. patric44

    A problem in solving Schrodinger equation for hydrogen

    hi guys i am having a little problem concerning the theta part of TISE : its clearly that its very similer to the associated Legendre function : how iam going to change 1/sinθ ... to (1-x^2) in which x = cosθ i tried many identities but i am stuck here . any help on that ?
  42. S

    I Did Erwin Schrödinger propose that reality could be contradictory?

    Did Schrödinger believe that contradictory or inconsistent things could exist in reality?
  43. Diracobama2181

    A Gauge Invariance of the Schrodinger Equation

    Given the schrodinger equation of the form $$-i\hbar\frac{\partial \psi}{\partial t}=-\frac{1}{2m}(-i\hbar \nabla -\frac{q}{c}A)^2+q\phi$$ I can plug in the transformations $$A'=A-\nabla \lambda$$ , $$\phi'=\phi-\frac{\partial \lambda}{\partial t}$$, $$\psi'=e^{-\frac{iq\lambda}{\hbar c}}\psi$$...
  44. P

    Solutions to schrodinger equation with potential V(x)=V(-x)

    C is just the constant by ##\psi''## My initial attempt was to write out the schrodinger equation in the case that x>0 and x<0, so that $$ \frac {\psi'' (x)} {\psi (x)} = C(E-V(x))$$ and $$ \frac {\psi'' (-x)} {\psi (-x)} = C(E-V(-x))$$ And since V(-x) = V(x) I equated them and...
  45. GeolPhysics

    I Schrodinger equation for a free particle in 3d space

    I've got the solution to the question but I just need more detail. I can't work out the first step of the solution to the second step. That should read, I don't know what they multiplied ih-bar by to make it (i/h-bar)^2?
  46. TeethWhitener

    I How does the von Neumann equation relate to Schrödinger's equation?

    I was trying to show how to get Schrödinger’s equation from the von Neumann equation and I’m not quite confident enough in my grasp of the functional analysis formalism to believe my own explanation. Starting from $$i\hbar\frac{\partial}{\partial t}\rho=[H,\rho]$$ We have...
  47. medofx

    Help please (concerning eigenfunctions and the Schrödinger equation)

    i have an exam in 2 days and in this question i don't know how should i proceed after that i simplified the wave function but i don't know how to confirm that it's an eigenfunction