Schrödinger Definition and 591 Threads

  1. Orion1

    Massless Schrödinger equation

    A massless particle situated in a 1D infinite square well with momentum only in the direction of quantum confinement (the x direction): E_t \psi (x) = \hbar \omega \psi (x) = i \hbar \frac{\partial}{\partial t} \psi (x) p(x) \psi(x) = \hbar k_x \psi (x) = -i \hbar \frac{\partial}{\partial x}...
  2. B

    Last step of a Schrodinger derivation

    I have looked at several derivations of the Schrodinger equation but the one I like the best is from Piravonu Mathews and K. Venkatesan in their book ‘A Textbook of Quantum Mechanics’. I follow their logic and algebra up until the last step were they arrive at the Schrodinger equation for one...
  3. K

    Why did Schrodinger call his equation eigenvalue problem?

    Why did Schrodinger call his equation eigenvalue problem? We can solve Schrodinger equation since it's just differential equation with complex number
  4. T

    About Schrodinger eq. and the potential step case with E = V0

    I have a simple question but can't find the answer: What happens in the Potential Step (the Schrodinger Equation aplication) case when E = V0 ? I only seem to find the cases when E>V0 or E<V0. Thanks in advance!
  5. redtree

    Probability amplitudes, de Broglie and Schrödinger

    What is the relationship between the "matter waves" described by de Broglie, the probability amplitude function and Schrödinger's wave equation? I've read the following: "The wavelengths postulated by de Broglie to be associated with the motions of particles are in reality the wavelengths...
  6. B

    What is the meaning of the lower case i in the Schrodinger equation?

    When examining the Schrodinger equation for a particle in a square well there is a lower case “i” that shows up in the equations that never gets defined. I have checked several sources and its usage is somewhat uniform and yet not defined. Can someone define the “i” ? One source I am...
  7. A

    Probability distribution of stationary Schrodinger equation

    Homework Statement Stationary Schrodinger equation for a particle moving in a potential well has two solutions psi1(x)=e^-ax^2 with energy E1 and psi2(x)xe^-ax^2 with energy E2 At t=o, the particle is in the state psi(x)=psi1(x)+psi2(x) Calculate the probability distribution as a...
  8. B

    Energy levels from the Schrodinger eqn

    Homework Statement I'm just wondering how you get the energy levels from the Schrodinger equation. I've got the equation in the form H(psi) = E(psi) with all the H expanded out, I just don't know how to calculate the energy levels from it. Its probably something I did once know how to do, but...
  9. R

    Solving the Schrodinger Equation for the Harmonic Oscillator in Momentum Space

    How can I write the Schrodinger equation for the harm. oscillator in momentum space and then solve it? Thank you, in advance:)
  10. C

    Solution for schrodinger equation

    In the potential well example we are considering the potential in the well to be zero and infinite outside the boundary, does this mean that the electron can move freely such that there is no opposition or restoring energy acting on it. And also the probability of finding the electron is...
  11. B

    Momentum operator in Schrodinger equation

    Why momentum is replaced by momentum operator in Schrodinger equation ?
  12. C

    Schrodinger equation graph help

    I hope I'm not offending anyone here by posting a request for some help here. We are in need of a knowledgeable physicist who can interpret an anomoly in a Schrodinger equation graph. This is for an online alternate reality game ("ARG") called Find the Lost Ring. The graph can be found here...
  13. Z

    1-d Time Independent Schrodinger Equation Problem

    Homework Statement A particle of mass m and energy E, where E >V1 >V2 travels to the right in a potential defined as V(x) = V1 for - b < x < 0 V(x) = 0 for 0 < x < a V(x) = V2 for a < x < b (a) Write down the time-independent Schrodinger eq. and its general solution...
  14. C

    Time-dependant Schrödinger Equation Help.

    I have a project to work on that's due by mid March. I would need to write a computer program, to show how a wave packet reflect off a barrier? How much of the wave reflects off a wall of finite height and thickness, and how much tunnels through? I remember doing something similar in my...
  15. R

    How to Solve the Dimensionless Schrodinger Equation for a Wave Function?

    Hi I am new to quantum physics and i have been asked to find the dimensionless schrodinger EQ for a wave function it says sub in t = (2/ohm)*tor and x = sqrt(h-bar/m*ohm)z now do i just put in these values and diffreinchiate threw ? or is it more complex ? thank you for your time Ross Taylor
  16. JasonGodbout

    Angular equation (schrodinger)

    [SOLVED] angular equation (schrodinger) Hi, I don't now how to pass from the form1 to Associated legendre fuction (form2) in the attache file .doc Someone can help me? Thanks :)
  17. N

    Calculate time evolution of Schrodinger wave equation

    [SOLVED] Calculate time evolution of Schrodinger wave equation Homework Statement At time t=0 particle is in state: \psi\left(x\right)=\sqrt{2}A\phi_{1}(x)+\frac{A}{\sqrt{2}}\phi_{2}(x)+A\phi_{3}(x) where \phi_{n}(x) are eigenfunctions of 1-D infinite potential well. a) Normalize...
  18. B

    What is the PDE for photons proposed by Bialynicki-Birula?

    Neither in Sam Treiman's http://books.google.de/books?id=e7fmufgvE-kC" I was able to find the Schrödinger equation for a photon, i.e. a particle without rest mass. The Schrödinger equation straight from Treiman's book (typos are mine, if any) -\frac{\hbar^2}{2m}\Delta\Psi + V\Psi =...
  19. T

    Schrödinger equation: eigen value or differential equation

    I have a problem on the basis of quantum mechanics and it's so simple that I'm almost too afraid to ask. Anyway: 1.) Schrödingers differential equation is used for time indepent and time depent problems. The solution is a wave function or the linear combination of the resulting wave...
  20. C

    How to Find the Ground State Energy Using the Shooting Method?

    Homework Statement The wave function of a particle satisfies the time-independent schrodinger equation. If the potential is symmetric and has the form V(x) = \inf |x|>1.0 V(x) = \frac{\hbar^2V_0}{2m} |x|<0.2 V(x) = 0 Elsewhere Using the shooting method, I need to find the...
  21. D

    Physical Chemistry, P.W.Atkins, the Schrödinger equation

    Homework Statement Im doing an A-level project on the Schrödinger equation and am unsure on the mathematics used to obtain the following results: The Schrödinger for a particle in no potential field (=0) has the solution: psi(x)=e^ikx. i is defined below, I haven't really a clue as to...
  22. P

    Time-Dependent Schrodinger Equation

    Homework Statement Show that \Psi(x,t) = Ae^{i(kx-\omega t)} is a solution to the time-dependent Schrodinger equation for a free particle [ U(x) = U_0 = constant ] but that \Psi(x,t) = Acos(kx-\omega t) and \Psi(x,t) = Asin(kx-\omega t) are not. Homework Equations - \frac{h^2}{4\pi...
  23. A

    Schrödinger equation: macro level

    Is it possible, in theory, to describe a macroscopic object with the Schrödinger equation (its location for example)?
  24. R

    Another question on Schrodinger Equation

    I have read the following claim (where is not important): ...the Schrodinger equation provides no rational basis for the phenomenon of spin, the Pauli Exclusion Principle, or Hund's Rule... Is such a claim true ? If so, what does it matter ?
  25. D

    Solving 1D Schrodinger Eq. for Energies < V0

    For the well shown below (Attachment or Link belew) solve the time independent one dimensional Schrodinger equation for energies less than V0. You may (and should) leave your answer in terms of a single transcendental equation for the allowed wave numbers. \frac{-\hbar^2}{2m} ...
  26. Pythagorean

    Time-Dependent Schrodinger Eq: Integrating Time?

    My own question, carried to a new thread as not to derail another:
  27. P

    Schrodinger equation with Electric/Magnetic Potential

    Homework Statement Consider a particle of charge e and mass m in crossed E and B fields, given by E = (0,0, E), B = (0,B, 0), r = (x, y, z). Write the Schrodinger equation. Homework Equations Schrodinger's equation: \left[ -\frac{\hbar^{2}}{2m} \nabla^{2} + V(r,t) \right] \Psi(r,t)...
  28. H

    Slow variables in Nonlinear Schrodinger Equation

    Hi all. What do it mean by "slow variables" in NLS? I am reading a derivation of the NLS in the context of hydrodynamics, by R.S.John in his book "A modern introduction to the Mathematical Theory of Water Waves". In the book, slow variables are zeta = epsilon * (x-ct) and T = epsilon * t...
  29. E

    Dimensionless form of the time-independent Schrodinger equation

    For a free particle, show that the time-independent Schrodinger equation can be written in dimensionless form as d^2\psi(z)/dz^2 = -\psi(z) . I do not see how you would get rid of the m (with units mass) in front of the del in the SE (or the other constants for that matter)...
  30. E

    Solution to the Schrodinger Equation

    I am somewhat confused about how general the solution \psi_E(x) = Aexp(ikx)+Bexp(-ikx) is? Can someone complete one or both of these sentences: \psi_E(x) = Aexp(ikx)+Bexp(-ikx) is the solution to all equations of the form ... or \psi_E(x) = Aexp(ikx)+Bexp(-ikx) is a...
  31. R

    Where Can I Find Solutions for 3D Schrödinger Equation?

    Hello everyone! I am a new member and please sorry for some question that perhaps were discussed here before. But really I need your help. I am searching for methods of solving 3 dimensional Schrödinger equation. Till now in internet I coulnd't find any solution. All the papers and articles are...
  32. T

    Time independent schrodinger equation: delta potential

    I'm currently reading Griffith's book on time independent Schroedinger's equation about delta functions. However, I complete dislike how the book deals with the delta distribution. firstly, the book discusses how to solve: -\frac{\hbar^2}{2m}\frac{d^2\psi}{dx^2}-\alpha\delta\psi=E\psi for...
  33. B

    Can someone explain the Schrödinger equation?

    Sorry, I'm new, can someone provide a simplified (i.e. dumbed-down) explanation of the Schrodinger equation? i understand some of the basics of quantum mechanics, and i find this thread fascinating. at the base level, this seemed like a fairly straightforward question, but it seems there are...
  34. M

    Schrödinger eq. with 3D spherical potential

    Hello! I'm trying to solve some old exam exercises to prepare for my qm exam next week. Now I got a question I don't have any idea how to solve it. I hope somebody can help me: "The radial Schrödinger equation in the case of a 3D spherical symmetric potential V(r) can be written in the...
  35. A

    How is the conjugate momentum defined in the Schrödinger picture of QFT?

    Hi, I have been wondering why we can consider d(phi)/dt when we are in Schrödinger picture (phi is just the usual scalar field here). Isn't this 0 as operators do not depend on time in this picture? However then how does it make sense to talk about the conjugate momentum in this picture which...
  36. M

    Schrodinger eqn. and its relativistic generalisations

    I've suddenly run into a problem. This has probably arisen from the fact that I've yet to have (and may never have) formal teaching on the relativistic generalisation of QM. I see the Schrodinger equation proper as \hat{H}| \psi (t) \rangle = i\hbar \frac{d}{dt} | \psi (t) \rangle Is this...
  37. S

    Bound states for a Spherically Symmetric Schrodinger equation

    Homework Statement A particle of mass m moves in three dimensions in a potential energy field V(r) = -V0 r< R 0 if r> R where r is the distance from the origin. Its eigenfunctions psi(r) are governed by \frac{\hbar^2}{2m} \nabla^2 \psi + V(r) \psi = E \psi ALL in spherical coords...
  38. S

    Question about schrodinger equation

    Note that this is not homework... I am just curious The time independant Schrodinger equation can be written as \hat{H} \psi = E\psi IS there ever a time taht the above equation is not true?? what about the time dependant case?? We haven't gone over that in class so I am not quite...
  39. Q

    Schrodinger equation in the spherical coordinates

    If using spherical coordinates (r, theta, phi) , what is the meaning of the canonical momentum of theta, phi? What are their definitions and mathematical form? In solving the Hydrogen problem, one has not take into consideration P_theta and P_phi at all. Quantum River
  40. B

    Eigenstates and eigenfunctions and Schrodinger - HELP PLEASE

    A couple of things first - Whats an eigenfunction? Whats an eigenvalue? I've been doing a course on quantum mechanics for nearly 2 months and whilst these words have popped up in both notes and lectures no-one has actually bothered to explain what they are or what they mean! Next thing. Can...
  41. L

    Solving Schrodinger for eingenvalues

    I'm looking to solve schrodingers equation for the bound energy state energy eigenfunctions, for a particle in a 1-D potential well (E<Vo), where; V(x)= (inf, x<0) (0, 0<x<a) (Vo, x>a)so we know when x>a our function is going to be a negative exp, and between 0 and a the function is...
  42. J

    Schrodinger equation Eigenfunction problem

    So, here's the question: \psi(x) = A*(\frac{x}{x_{0}})^n*e^(\frac{-x}{x_{0}}) Where A, n, and X0 are constants. Using Schrodinger's equation, find the potential U(x) and energy E such that the given wave function is an eigenfunction (we can assume that at x = infinity there is 0...
  43. S

    Delta function potential and Schrodinger Equation

    I have a time dependent wavefunction for inside a delta function potential well: V(x) = -a delta(x). It reads Psi(x,t) = (sqrt(m*a)/hbar) * exp(-m*a*abs(x)/hbar^2) * exp(-iEt/hbar) I'm supposed to stick this back into the time dependent Schrodinger Equation and solve for E. Taking my...
  44. D

    Linearity of Schrodinger Equation

    Could someone please address this question? How do you algebraically demonstrate the superposition principle revealed by the Schrodinger equation (ie. If Psi1(x,t) and Psi2(x,t) are both solutions then Psi(x,t)= Psi1(x,t)+Psi2(x,t) is also a solution.)?
  45. S

    Schrodinger Equation HELP: Find Energy Emitted by Photon in Infinitely Deep Well

    HELP! I need to find the energy emitted by a photon if an electron is confined in an infinitely deep well. Can someone tell me what the hell to do please?! I'm desperate! Thanks!
  46. Useful nucleus

    Finding Schrödinger & De Broglie's 1926 Quantum Physics Papers

    I have just read that Schrödinger had wrote six research papers ( in 1926) in which he presented the complete mathematical foundation of nonrelativistic quantum mechanics . Also read that De Broglie supported his proposal (the duality) by a proof derived from relativity theory . Are these...
  47. L

    Who Was the First to Use Wave Mechanics to Study Electrons in the Hydrogen Atom?

    Here is an objective question: The first full presentation of the behavior of electron in hydrogen atom by using wave mechanics is by: Louis de Broglie or Schrodinger? As far as I know, Schrodinger is famous for his wave equation. Meanwhile, de Broglie is known for the equation lambda= h/mv.
  48. S

    How Does the Schrödinger Equation Govern the Time Dependence of Wave Functions?

    By noting that the time dependence of the wave function is governed by the Schrodinger equation show that \frac{d(\Psi^* x \Psi)}{dt} = \frac{i \hbar}{2m} \left[x\Psi^* \frac{d^2\Psi}{dx^2} - x \Psi \frac{d^2 \Psi^*}{dx^2} \right] not sure where to start on this one actually... do i start...
  49. B

    Solution of 1D Schrodinger using discretized hamiltonian

    Hi all, I'm trying to solve the 1D Schrodinger equation for an arbritary potential, to calculate Franck Condon factors for absorption and emmision spectra. I can do this using iterative techniques (e.g. the Numerov method), but I can't seem to get it to work by discretrizing the hamiltonian...
  50. E

    Schrodinger equation in gravitational field

    I read article http://www.oup.co.uk/pdf/0-19-850687-2.pdf There is described Schrodinger equation in gravitational field (1.10) and COW experiment. But once I found article, where it is shown that this Schrodinger equation is in direct contradiction with principle of equivalence. Can...
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