What is Schrodinger equation: Definition and 564 Discussions
The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of the subject. The equation is named after Erwin Schrödinger, who postulated the equation in 1925, and published it in 1926, forming the basis for the work that resulted in his Nobel Prize in Physics in 1933.Conceptually, the Schrödinger equation is the quantum counterpart of Newton's second law in classical mechanics. Given a set of known initial conditions, Newton's second law makes a mathematical prediction as to what path a given physical system will take over time. The Schrödinger equation gives the evolution over time of a wave function, the quantum-mechanical characterization of an isolated physical system. The equation can be derived from the fact that the time-evolution operator must be unitary, and must therefore be generated by the exponential of a self-adjoint operator, which is the quantum Hamiltonian.
The Schrödinger equation is not the only way to study quantum mechanical systems and make predictions. The other formulations of quantum mechanics include matrix mechanics, introduced by Werner Heisenberg, and the path integral formulation, developed chiefly by Richard Feynman. Paul Dirac incorporated matrix mechanics and the Schrödinger equation into a single formulation. When these approaches are compared, the use of the Schrödinger equation is sometimes called "wave mechanics".
If
H1=P^2/2m+V1(x), H2=P^2/2m+V2(x), H=P^2/2m+V1(x)+V2(x)
and
H1 f1_i(x)=E1_i*f1_i(x),
H2 f2_j(x)=E2_j*f2_j(x),
H f_k(x)=E_k*f_k(x)
Is there any relation between f1_i(x),f2_j(x),f_k(x)?Can we express f_k(x) in terms of f1_i(x) and f2_j(x)?
I am trying to find the Schrodinger's equation for the one-dimensional motion of an electron, not acted upon by any forces.
So.. should I begin using the time independent form of the Schrodinger's equation? What should I arrive at? Should I let my V(x) = 0?
Also, how do I show that...
Ok, I know that the 1D time-independent Schrodinger equation is -\frac {\hbar^2} {2m} \frac {d^2 \psi(x)} {dx^2} + V(x) \psi(x) = E \psi(x). Why is it that you can mix potentials and energies in the same equation? For example, if you're saying that V(x) has a constant value, say, V(x) = V_{0}...
can you explain this statement "if psi is a solution of a schrodinger equation, then so is kpsi, where k is any constant".
why is that multplying psi by a constant does not its value?
Hi, I have a problem.
I want to show that
\frac{d}{dt} \int_{-\infty}^{\infty} \psi_1^{*}\psi_2 dx = 0
for any two (normalizable) solutions to the Schrödinger equation. I have tried rearranging the Schrödinger equation to yield expressions for \psi_1^{*} and \psi_2 like this...
:confused: Newton's equation (F=ma) could derive from Lagrangian, My question is, could we derive the schrodinger equation from the more fundemantal principle in Physics...
In the very first pages of "Quantum Mechanics" by Landau & Lifchitz, the measurement process is described as an interaction between a quantum system and a "classical" system.
I like this interpretation since any further evolution of the quantum system is anyway entangled with the "classical"...
One solution to the time-independent Schrödinger equation for a free particle (moving in 1 dimension) is:
\psi(x) = Ae^{ikx}
This has a definite momentum p = h-bar*k, but it can't be normalized since:
\int_{-\infty}^{\infty}\lvert\psi(x)\rvert^2dx = \int_{-\infty}^{\infty}|A|^2dx =...
Ok, so suppose there is a free particle of mass m that moves in a one-dimensional space in the interval 0<=x, with energy E. There is a rigid wall at x=0. Write down a time independent wave function G(x) which satisfies these conditions, in terms of x and k, where k is the wave vector of motion...
one-dimensional Schrodinger's Equation
Hi !
I wonder how to solve one-dimensional Schrodinger's Equation :
\frac{d^2 \psi (x)}{dx^2}\ = \ -(\frac{2 \pi}{\lambda})^2 \ * \ \psi (x)
I've to obtain \psi (x) , when
-(\frac{2 \pi}{\lambda})^2 is known
Can you solve it as an example...
I am looking for a detailed step by step derivation of the Schrodinger Eqn. where one will obtain the general solutions for R, Thetha, and Phi for the hydrogen atom. If someone could direct me to a reference of these derivations explained step by step it would be of great help.
[b(] --Wall...
I'm dong a presentation and I'm trying to explain how to use the Schrodinger Equation to find the wave function of a particle. And I have never done that before...I have a basic idea, but to be more accurate, I need you guys' help. Note that this is for a 7th grade class presentation (so if...