What is Time-independent: Definition and 43 Discussions

In computing, position-independent code (PIC) or position-independent executable (PIE) is a body of machine code that, being placed somewhere in the primary memory, executes properly regardless of its absolute address. PIC is commonly used for shared libraries, so that the same library code can be loaded in a location in each program address space where it does not overlap with other memory in use (for example, other shared libraries). PIC was also used on older computer systems that lacked an MMU, so that the operating system could keep applications away from each other even within the single address space of an MMU-less system.
Position-independent code can be executed at any memory address without modification. This differs from absolute code, which must be loaded at a specific location to function correctly, and load-time locatable (LTL) code, in which a linker or program loader modifies a program before execution so it can be run only from a particular memory location. Generating position-independent code is often the default behavior for compilers, but they may place restrictions on the use of some language features, such as disallowing use of absolute addresses (position-independent code has to use relative addressing). Instructions that refer directly to specific memory addresses sometimes execute faster, and replacing them with equivalent relative-addressing instructions may result in slightly slower execution, although modern processors make the difference practically negligible.

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  1. cwill53

    Question on Time-Independent Perturbation Theory

    I'm currently reading this passage to review perturbation theory. Just before Equation (A.4), this passage tells me to take the inner product of the proposed eigenstate ##|\psi _j\rangle## with itself. Writing this out, I got: $$1=\left \langle \psi _j| \psi _j\right \rangle=\left ( |\psi^0...
  2. 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?
  3. F

    I Uncertainty principle##\Delta H\Delta Q##, where Q is time-independent

    Let Q be a time-independent operator. ##[H,Q] = iħ[\frac{d}{dt},Q]## Since Q is time-independent, ##[H,Q]=0## And from the uncertainty principle : ##\Delta H\Delta Q \ge |<\Psi|\frac{1}{2i}[H,Q]|\Psi>|## From ##[H,Q] = 0##, I concluded that ##\Delta H\Delta Q \ge 0## But by evaluating d<Q>/dt...
  4. 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...
  5. eloiseh

    Find potential energy using time-independent Schrodinger's equation

    I had found what U(x) was equal to already by plugging in the wave function and simplifying, which is (2h^2/mL^4)(x^2 - 3L^2/2) by the way. But the solution key that I have goes an extra step. After stating the equation of U(x) that I got, it says that: "U(x) is a parabola centred at x = 0 with...
  6. jk22

    A GR: Is Schwarzschild Spacetime Time-Independent?

    I'm a bit confused about GR : what is more significant about the considered spacetime, the metric, which is time-independent, or the embedding (there are already some posts on PF about it), which describes the shape of a manifold, but is time-dependent ?
  7. G

    I General solution to the Time-independent Schrödinger equation?

    Has anyone formulated a general solution to the time-independent Schrödinger equation in terms of the potential function V(r), and if so, what is it? For any type of V(r). So, instead of a differential equation, a direct relationship between the wavefunction and the potential.
  8. D

    Finding Stationary Wavefunction with a Line Potential

    Homework Statement A particle of mass m in one dimension has a potential: $$V(x) = \begin{cases} V_0 & x > 0 \\ 0 & x \leq 0 \end{cases} $$ Find ##\psi(x)## for energies ##0 < E < V_0##, with parameters $$k^2 = \frac{2mE}{\hbar^2}$$ and $$\kappa^2 = \frac{2m(V_0 - E)}{\hbar^2}$$...
  9. S

    Simulating 1D time-independent Bose Einstein Condensation

    Hello! I'm trying to simulate a one dimensional time independent BEC, I hope this is the right place to ask for help. First of all, here's my code in Python. import sys import numpy as np import matplotlib.pyplot as plt if len(sys.argv) == 1: niter = 100 elif len(sys.argv) == 2: niter...
  10. W

    Time-independent Schrödinger equation, normalizing

    Homework Statement An electron coming from the left encounters/is trapped the following potential: -a<x<0; V=0 0<x<a; V=V0 infinity elsewhere the electron has energy V0 a)Write out the wave function b)normalize th wave function Homework EquationsThe Attempt at a Solution for -a<x<0...
  11. G

    Time-Independent Perturbation Theory

    Homework Statement I am working on a physics project for which I need to use perturbation theory to calculate the first- and second-order corrections to the eigenvalues and eigenvectors of a perturbed matrix. The unperturbed matrix is real and symmetric, and the eigenvalues and eigenvectors are...
  12. L

    I Tunnel Effect in Quantum Mechanics: Exploring Time-Independent Problems

    In case of tunnel effect in quantum mechanics we often consider time independent Schroedinger equation with potential ##0##, when ##x<0## then some ##V_0## when ##0\leq x\leq a## and ##0## when ##x>a## so potential barrier problem. And energy of particle that we send to barrier is ##E<V_0##. In...
  13. Z

    What makes localized energy eigenstates, localized?

    I'm reading about stationary states in QM and the following line, when discussing the time-independent, one-dimensional, non-relativist Schrodinger eqn, normalization or the lack thereof, and the Hamiltonian, this is mentioned: "In the spectrum of a Hamiltonian, localized energy eigenstates are...
  14. Rimmonin

    Is there a space-independent Schrödinger equation?

    I'm learning about the Schrödinger equation in one of my uni courses, and we've recently gone past how to solve the time-independent version. That got me wondering if there is a space-independent version of the Schrödinger equation and what it could possibly be used for. I know I'm probably...
  15. gfd43tg

    Time-independent SE linear combination solution help

    Hello, I am trying to derive the TISE, but I am having many questions, and the textbook (Griffiths) does not give any adequate explanation and I have minimal access to my professor. My goal is to find ##\Psi (x,t)##. The book says the solution is $$ \Psi (x,t) = \sum_{n=0}^{\infty} c_{n}...
  16. R

    Time-independent Schrodinger equation in term of the TDSE

    Homework Statement Write down the general solution of the time-dependant schrodinger equation in terms of the solutions of the time-independant Schrodinger equation. Homework Equations TDSE TISE The Attempt at a Solution I'm really not sure how to interpret this question, I could write the...
  17. P

    State Space: time dependent states but time-independent output

    Let: $$x_1=A\sin{\omega t}$$ $$x_2=\dot{x}_1=A\omega \cos{\omega t}$$ $$y=A\omega$$ We want to represent this system in a state space model. The state transition matrix read: $$A=\begin{bmatrix} 0 & 1 &\\ -\omega^2 & 0 \\ \end{bmatrix}$$ I am not sure what the output matrix will be like. Can we...
  18. M

    How to find the time-independent (unnormalized) wavefunction

    Homework Statement How would I find the time-independent (unnormalized) wavefunction given the momentum? I don't know if this can be generalized without giving the momentum in the problem. I want to do this problem myself but I'm stuck. The problem states: A particle of mass m moves...
  19. W

    How do we know E is energy in the time-independent Schrodinger eq

    Hi everyone, One approach to solve the Schrodinger equation is to use separation of variables: the solution is composed of a time dependant and space dependant component. When we go through the math, we get a time dependent LHS equal to a space dependant RHS, which means they must both be...
  20. TrickyDicky

    Dynamic solutions in time-independent spacetimes

    Hi, I would like to clarify this probably trivial little issue that is bugging me: How should dynamical solutions be understood in the context of a static spacetime? To exemplify what I mean I'll use a well known case, the source-free Maxwell eq. in their explicitly covariant form set in...
  21. D

    Simple time-independent non-degenerate quantum perturbation

    I'm reading through this pdf (http://www.pa.msu.edu/~mmoore/TIPT.pdf) on simple quantum perturbation theory and I'm quite confused with equations 32 through 34. They have E_{n}^{(2)} = <n^{(0)}|V|n^{(1)}> = - \sum_{m \neq 0}{\frac{|V_{mn}|^{2}}{E_{mn}}} but I would have done E_{n}^{(2)} =...
  22. M

    Stationary States and time-independent states (aren't they the same?)

    I always thought they were the same, but now I am reading a question that says "which of he following time-independent functions describe stationary states of the corresponding quantum systems?" Is there something I am missing? It's written like there is something to solve, but to me it seems...
  23. G

    Klein-gordan Hamiltonian time-independent?

    How can you tell if the Klein-Gordan Hamiltonian, H=\int d^3 x \frac{1}{2}(\partial_t \phi \partial_t \phi+\nabla^2\phi+m^2\phi^2) is time-independent? Don't you have to plug in the expression for the field to show this? But isn't the only way you know how the field evolves with time is...
  24. 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...
  25. B

    Specific question on Goldstein section on Time-independent perturbation theory

    I apologize that this is rather specific, but hopefully enough people have used Goldstein. I have a basic grasp of action-angle variables, and I'm going through the time-independent perturbation theory section in Goldstein (12.4). In this section we seek a transformation from the unperturbed...
  26. N

    Exploring Time-Independent Force in QM

    Homework Statement Hi In QM we define the force operator F as (in the Heisenberg picture) F = \frac{1}{i\hbar}[p, H] + (d_t F)(t) What I can't understand is that usually (actually, always) we write F = \frac{1}{i\hbar}[p, H] and neglegt the last time derivative. How can we be so certain...
  27. A

    Question on time-independent perturbation theory

    Hi all. I have been thinking about a very simple question, and I am a little confused. We know from time-independent perturbation theory that if the system is perturbed by the external perturbation λV which is much smaller compared to the unperturbed hamiltonian H0, we can write the ground state...
  28. R

    Time-independent Schrodinger Equation

    Why is it that we assume that the solutions to the time-independent Schrodinger Equation are real? Why can't they be complex?
  29. C

    Time-Independent Schrödinger Equation

    How can time-independent schrödinger equation be proven? Do you know any source which explains it clearly? Thanks for replies.
  30. X

    Potential function for the Time-Independent Schrodinger eq.

    Homework Statement [PLAIN]http://img820.imageshack.us/img820/4205/agvg.png Homework Equations TISE: \left(-\frac{\hbar}{2m}\nabla^2 + V(r) \right) \psi(r) = E\psi(r) The Attempt at a Solution Can someone tell me what 'transcendental' means in part b). I've...
  31. X

    Solutions of of the time-independent Schrodinger eq.

    Homework Statement Supposed that \psi1 and \psi2 are two different solutions of the TISE with the same energy E. a) show that \psi1 + \psi2 is also a solution with energy E. b) show that c*\psi1 is also a solution with energy E. Homework Equations TISE: (-\hbar/2m)*\nabla^2*\psi(r)...
  32. C

    Energy eigenfunctions in time-independent perturbation theory

    I've been working my way through some basic quantum mechanics, and have gotten up to perturbation theory. It basically makes sense to me, but there's one thing that bothers me, and I was wondering if somebody could shed some light on it. The essential idea behind perturbation theory is that we...
  33. A

    Question on Time-independent perturbation theory: I am confused

    We all know from time-independent perturbation theory that if we have an atom in ground state [0>, and when a time-independent perturbation acts on it, the energy of the ground state gets shifted and the ground state wave function also gets modified. Using Time-independent Schroedinger eq...
  34. 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...
  35. A

    Simple time-independent perturbation problem. QM

    Homework Statement "Suppose we put a delta-function in the center of the infinite square well: {H^{'}} = \alpha\delta(x-a/2) where a is a constant. Find the first order correction to the allowed energies. Explain why the energies are not peturbed for even n" Homework Equations The...
  36. S

    Time-independent Schrödinger Equation

    Hi everyone, I have been studying Quantum mechanics course for one month and our subject for now is Time-independent Schrödinger Equation. What I couldn't figure out is whether \Psi(x,\,0) = \Psi(x), since \Psi(x,\,0) doesn't contain any time dependence and \Psi(x) as well. Can someone explain...
  37. D

    Constructing time-independent wave function with given energies

    Does anyone know how to construct a Time-independent wave function with given energies and probability on obtaining energies.
  38. D

    Time-independent wave function formula

    Homework Statement Construct wavefunction with given energies and probabilities of obtaining energies in a 1-D box from 0 to aHomework Equations [b]3. The Attempt at a Solution I know the general form of a time-independent wavefunction but I don't know what to do with the probabilities of...
  39. C

    Solving the Time-Independent Schrödinger Equation for a Step Potential

    Considering a step potential of V(x) = o when x<o and V(x) = Vo when x>o so step occurring at origin of x axis. Write down in words the strategy for solving it. Answer: Solve the time-independent schrodinger equation for V=o when x<o and find the solution for the free particle wave function...
  40. E

    Time-independent perturbation theory

    Homework Statement In each of my QM books, they always say something like "we can write the perturbed energies and wavefunctions as" E_n = E_n^{(0)} + \lambda E_n^{(1)} + \lambda^2 E_n^{(2)} + \cdots |n\rangle = |n^{(0)}\rangle + \lambda |n^{(1)}\rangle + \lambda^2 |n^{(2)}\rangle + \cdots...
  41. 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)...
  42. E

    Time-Independent Perturbation Theory

    Hi, I'm working out the 2nd Edition of Quantum Mechanics by Bransden & Joachain and I'm a little puzzled by the sign of the last term in equation 8.30 on page 380, which reads... a_{nl}^{(2)} = \frac{1}{E_n^{(0)} - E_l^{(0)}}\sum_{k{\neq}n} \frac{H_{lk}^{'}H_{kn}^{'}}{E_n^{(0)} - E_l^{(0)}}...
  43. D

    Time-independent wavefunction

    I have a problems, help me please a) A free particle of mass m moves in one-dimensional space in the interval 0 <= x, with energy E. There is a rigid wall at x = 0. Write down a time-independent wavefunction, which satisfies these conditions, in term of x and k wher k is the wave vector of...