What is Schrodinger's equation?

Answer 1

The basic form of the equation comes directly out of Hamiltonian mechanics:

H = K + V

where H is the Hamiltonian, K is kinetic energy, and V is potential energy. K can be restated as p^2/2m, where p is momentum, so that we have

H = p^2/2m + V

In quantum theory, H and p are replaced with operators, so ft hat for a state function W(x,t), we have (for 1D case):

H (W(x,t) = (p^2/2m + V(x,t)) (W(x,t)) =

ih d/dt (W(x,t)) = - h^2/2m d/dt d/dt (W(x,t)) + V(x,t) W(x,t)

Compare the form with the 1D diffusion equation from classical physics:

d/dt (W(w,t)) = k d/dt d/dt (W(w,t)) + V(x,t)

Since the classical diffusion equation describes the position probability of a random walk, it has been suggested by physicists like Feynman that Schrodinger's wave equation describes the position probability of a random walk in complex time, where

i t is substituted for t

The link below takes you directly to the core concepts of this equation.

Answer 2

Equation 3 Schrodinger's wave equation
This very important equation is a result of conservation of energy and the relations between total energy and w and between the momentum and the wave number, k. Remember that the wave function in equation 3 is the sum of waves in equation 2. Schrödinger’s equation is a 2nd order partial differential equation that is linear. Each term in the summation in equation 2 is differentiated independent of the other terms. We can write a Schrödinger equation for each term of the sum of waves.
http://www.missioncollege.org/depts/physics/P4poe/P4D/Schrodinger.htm

Answer 3

i think what you want is the meaning of the equation. schodinger equation is used to get the wave function(psi). by the postulates of quantum mechanics any system is completely described by knowing psi. ie psi can mathematically give the value of any observable quantity like position, momentum etc. so we just need to know psi to theoretically calculate anything about the system.

so first we have to get the hamiltonian(energy) of the system(which depends on the potential of the system; hydrogen atom has coulomb potential, nuclear system has yukawa potential etc.). then we have the schodinger eqn.
(ih/(2pi)) dpsi/dt = H psi
solve the eqn and get the psi
use it to evaluate any observable theoretically.

Answer 4

its well....... cant ans on keyboard. But i'll try..
first d= doe [ it sounds doe but dont know if i got the spelling right]
s= sy [ sounds like that when u spell it]
the equation-
d square s/ d x square+ d sqare s/d y sqare + d sqare s/ d z sqare+ 8 pi sqare m= 0

Answer 5

have your self a merry little christmas night and a happy new year