Prize in Physics in . This equation which incorporates wave- particle duality of matter as proposed by de Broglie is quite complex and knowledge of higher mathematics is needed to solve it. You will learn its solutions for different systems in higher classes. For a system (such as an atom or a molecule whose energy does not change with time) the Schrödinger equation is written as where is a mathematical operator called Hamiltonian.
Schrödinger gave a recipe of constructing this operator from the expression for the total energy of the system. The total energy of the system takes into account the kinetic energies of all the sub-atomic particles (electrons, nuclei), attractive potential between the electrons and nuclei and repulsive potential among the electrons and nuclei individually. Solution of this equation gives E and ψ . Hydrogen Atom and the Schrödinger Equation When Schrödinger equation is solved for hydrogen atom, the solution gives the possible energy levels the electron can occupy and the corresponding wave function(s) ( ψ ) of the electron associated with each energy level.
These quantized energy states and corresponding wave functions which are characterized by a set of three quantum numbers ( principal quantum number n , azimuthal quantum number l and magnetic quantum number m l ) arise as a natural consequence in the solution of the Schrödinger equation. When an electron is in any energy state, the wave function Erwin Schrödinger, an Austrian physicist received his Ph.D. in theoretical physics from the University of Vienna in . In Schrödinger succeeded Max Planck at the University of Berlin at Planck’s request.
In , Schrödinger left Berlin because of his opposition to Hitler and Nazi policies and returned to Austria in . After the invasion of Austria by Germany, Schrödinger was forcibly removed from his professorship. He then moved to Dublin, Ireland where he remained for seventeen years. Schrödinger shared the Nobel Prize for Physics with P.A.M.
Dirac in . Erwin Schrödinger ( – ) corresponding to that energy state contains all information about the electron. The wave function is a mathematical function whose value depends upon