The Schrödinger wave equation cannot be derived (at least not by any known means). Erwin Schrödinger literally guessed the equation (though his guess had reason behind it), and justification for its use can be attributed to the simple fact that it works.
Thought it was guess when Schrödinger formulated his wave equation he drew from a classical foundation. Total energy is equal to the kinetic energy plus the potential energy. Classically kinetic energy is expressed as p2/(2m), where p is momentum and m is the mass. The potential can be whatever you want it to be so we will just call it V, then finally lets call the total energy E. We put this all together to get p2/(2m)+V=E but in terms of operators p=[i*h/(2*pi)]*(d2/dqi2), where i is the square root of negative one, h is Planck's constant, pi is 3.141529, and (d2/dqi2) is the second order differential with respect to space in generalized coordinates. So putting p back in our equation for energy we get [- h2/(4*pi*m)]*(d2/dqi2)+V=E. Now comes the sort of complex part. In general the total energy of a system is defined by the Hamiltonian, lets call is H. Now, E is the eigenvalue of the Hamiltonian operator. Meaning that when H operates on some state it is measuring the total energy of that state. In quantum mechanics H=[i*h/(2*pi)]*(d/dt), where (d\dt) is the first order differential with respect to time. Now putting this all together we get [i*h/(2*pi)]*(d/dt)=[- h2/(4*pi*m)]*(d2/dqi2)+V. That, to me, is Schrodinger's "picture" of the wave equation.
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Sorry it is a bit lengthy but I wanted to be thorough.
The time-independent Schr
Boundary conditions allow to determine constants involved in the equation. They are basically the same thing as initial conditions in Newton's mechanics (actually they are initial conditions).
Erwin Schrodinger
derive clausious mossotti equation
Yes it is
This is the Schrodinger equation from 1925-1926.
Schrodinger wave equation
That's really too complicated for a short answer, of a few paragraphs, here. YouTube has some introductory videos about the topic, for example, from a "Dr PhysicsA"; a search on YouTube for "Dr Physics Schrödinger Wave Equation" will let you find them.
equation is a double differential relate to the energy of particle with wave function
No, it is not solvable for any multi-electron system.
For general waves...probably d'Alembert, who solved the one-dimensional wave equation. In quantum it would have to be Schrodinger.
It is also called wave mechanics because quantum mechanics governed by Schrodinger's wave equation in it's wave-formulation.
The current picture of the hydrogen atom is based on the atomic orbitals of wave mechanics which Erwin Schrodinger developed in 1926. This model is based on the Schrodinger Equation.
1) What is the definition of dielectric permittivity on the basis of Maxwell equations? 2) What is Poisson equation of Electrostatics? Derive the Poisson equation from Maxwell equations. 3) Write the Biot-Savar equation. What is the meaning? 4) Derive a wave equation of a plain electromagnetic wave from Maxwell equation.
Schrodinger
The equation, as originally written by Erwin Schrodinger, does not use relativity. More complicated versions of his original equation, which do incorporate relativity, have been developed.For more information, please see the related link below.
The time dependent equation is more general. The time independent equation only applies to standing waves.