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.
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:
$$1=\left \langle \psi _j| \psi _j\right \rangle=\left ( |\psi^0...
Why you can do separation of variables in time-dependent
Schrödinger equation
i \hbar \frac{\partial \psi(\vec{r},t)}{\partial t}=-\frac{\hbar^2}{2m}\Delta \psi(\vec{r},t)+V(\vec{r})\psi(\vec{r},t)
with
\psi(\vec{r},t)=\varphi(\vec{r})T(t)
and when in general is that possible?
Let Q be a time-independent operator.
##[H,Q] = iħ[\frac{d}{dt},Q]##
Since Q is time-independent, ##[H,Q]=0##
And from the uncertainty principle :
##\Delta H\Delta Q \ge |<\Psi|\frac{1}{2i}[H,Q]|\Psi>|##
From ##[H,Q] = 0##, I concluded that ##\Delta H\Delta Q \ge 0##
But by evaluating d<Q>/dt...
I have to solve the 1D Time-independent Schrödinger equation (TISE) using the shooting algorithm. As far as I understood from this video on Shooting method for solving BVP, I will have to solve the problem by using IVP solvers (like RK2 or RK4 methods), and guess a value for the derivative of...
I had found what U(x) was equal to already by plugging in the wave function and simplifying, which is (2h^2/mL^4)(x^2 - 3L^2/2) by the way.
But the solution key that I have goes an extra step. After stating the equation of U(x) that I got, it says that: "U(x) is a parabola centred at x = 0 with...
I'm a bit confused about GR : what is more significant about the considered spacetime, the metric, which is time-independent, or the embedding (there are already some posts on PF about it), which describes the shape of a manifold, but is time-dependent ?
Has anyone formulated a general solution to the time-independent Schrödinger equation in terms of the potential function V(r), and if so, what is it?
For any type of V(r).
So, instead of a differential equation, a direct relationship between the wavefunction and the potential.
Homework Statement
A particle of mass m in one dimension has a potential:
$$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}$$...
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...
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...
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...
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...
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...
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...
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}...
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...
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...
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...
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...
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...
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)} =...
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...
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...
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...
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...
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...
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...
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...
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)...
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...
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...
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...
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...
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...
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...
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...
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...
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)...
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)}}...
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...