The Schrodinger equation The energy of a physical system is characterized by its

Question

The Schrodinger equation The energy of a physical system is characterized by its Hamiltonian H, which is the sum of its kinetic energy T and its potential energy T V. H-T+V The kinetic energy T of the system is defined only by the momentum P of its center of gravity for velocity ) and its mass T: The potential energy V in which the system evolves is only dependent on the position F of the system's center of mass in a conservative (no losses) environment. V(F) s representative of an energy state E of the system. They are solutions of the Schrodinger equation The energy o a quantum system can be described by a wavefunction an eigenvalue problem: t This wavefunction t or the system as The correspondence principle between the classical and the quantum use of the Hamiltonian transforms the momentum P and the energy E into operators on the wavefunction: Pe öy Solving the Schrodinger equation now means solving the differential equation:

Explanation / Answer

Down delta is actually symbol of d/dr hence down delta square is d^2/dx^2 the second derivative of wave function. Now this equation is differential equation of time dependent schrodinger's wave equation represent the wave nature. To solve this you can proceed by variable separable method of t and r. Spatial and temporal term will be psi(t) and psi (r) . Psi(r,t) = psi(r) e^(-iEt/) This is the general form of solution. h(cross) is h/2pai

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