Time-independent Definition and 44 Threads

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. Clvrhammer

    I Definition of time-independent scalar field in GR

    I was wondering how the notion of a time-independent field translates into the context of General Relativity. In order to specify my confusion, consider a scalar field ##\phi## in Schwarzschild spacetime with usual coordinates ##(t,r,\theta,\phi)##. Its metric is $$g = - f(r) \, dt^2 + f(r)^{-1}...
  2. 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...
  3. 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?
  4. 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...
  5. Wrichik Basu

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

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  6. eloiseh

    Find potential energy using time-independent Schrodinger's equation

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  7. jk22

    A GR: Is Schwarzschild Spacetime Time-Independent?

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  8. 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.
  9. D

    Finding Stationary Wavefunction with a Line Potential

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  10. S

    Simulating 1D time-independent Bose Einstein Condensation

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  11. W

    Time-independent Schrödinger equation, normalizing

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  12. G

    Time-Independent Perturbation Theory

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  13. L

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

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  14. Z

    What makes localized energy eigenstates, localized?

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  15. Rimmonin

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  16. gfd43tg

    Time-independent SE linear combination solution help

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  17. R

    Time-independent Schrodinger equation in term of the TDSE

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  18. 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...
  19. M

    How to find the time-independent (unnormalized) wavefunction

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  20. W

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

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  21. TrickyDicky

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  22. 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)} =...
  23. M

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  24. G

    Klein-gordan Hamiltonian time-independent?

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  25. A

    TIme-independent schrodinger equation

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  26. B

    Specific question on Goldstein section on Time-independent perturbation theory

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  27. 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...
  28. A

    Question on time-independent perturbation theory

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  29. 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?
  30. 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.
  31. 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...
  32. 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)...
  33. 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...
  34. 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...
  35. 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...
  36. 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...
  37. 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...
  38. 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.
  39. 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...
  40. 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...
  41. 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...
  42. 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)...
  43. 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)}}...
  44. D

    How Does a Rigid Wall Affect a Particle's Wavefunction in Quantum Mechanics?

    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...
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