Question

What is the Schrodinger Wave equation in orthogonal form?

Answer 1

Wave function can be regarded as vector in infinite dimensional linear vector space. To represent such vector we need an infinite dimensional space with orthonormal basis set of vectors. Generally, such basis set is set of eigen functions of Hermitian operator. These eigen functions corresponding to different eigen values are orthogonal ( perpendicular ) to each other. When they are normalized they behave as unit vectors in infinite dimensional linear vector space. A given wave function will have different representations in different basis set. The physical reality should be independent of coordinate system. So, for the general formalism we write the state vector irrespective of any coordinate system. Then ,we say the vectors as ket vectors in ket space. We also define the complex conjugate to ket vector and call them bra vector. |psi> is read as ket psi. And <psi| is called bra psi.
<phi|psi> is defined as scalar product if phi and phi. If <phi|psi>=0, then phi and psi are orthogonal to each other .

Answer 2

Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature T. The law is named after Max Planck, who proposed it in 1900. It is a pioneering result of modern physics and quantum theory.