Quantum Mechanics

Quantum mechanics provides a proper description of the mechanics of sub atomic particles such as electrons, protons, mesons etc. and quanta of light(photons). This subject has brought several new ideas to physics in our understanding of the microscopic world.

Planck's quantum nature of radiation:

Planck made following two radical assumptions about the atomic oscillators:

• An atom usually known as atomic oscillator, can't have any energy, but only energies given by
  E = nhν

  Where ν is frequency of oscillator, h is universal planck's constant, n is integer known as quantum number.

  the atomic oscillators do not radiate energy continuously but only discrete manner or quanta. These quanta of energy are emitted when an oscillator changes from one to another of its quantized energy states. Thus if n changes by one unit ,then from equation in 1.

  The amount of energy radiated is given by Δ E = Δ nh = ν

• hv (since Δ n = 1).

  As long as atomic oscillators remain in one of its quantized energy states , it neither emits nor absorbs energy. Thus according to planck's hypothesis, an atomic oscillator absorbs energy or gives off energy not in continuous steps , but in integral multiple of certain energy unit called quantum.

Wave function ( ψ ):

It is a highly complex valued function. ψ itself has no physical meaning but | ψ |² or ψ ψ*.dx.dy.dz proportional to probability of finding particle in certain volume element dx.dy.dz at a point x, y, z.

If we know we can determine physical properties of a system. Certain requirements of wave function are

• ψ should be normalized wave function.
• ψ should be single valued and continuous everywhere.
• δψ / δx, δψ / δy, δψ / δy, δψ / δz should be continuous and single valued everywhere.

Since | ψ |² evaluated at a point is proportional to the probality P Of finding the particle described by ψ at that point, the intergral of |ψ|² over all space must be finite-the particle is somewhere,after all. If is 0, the particle does not exist,and if it is ∞,  the particle is everywhere simultaneously,|ψ| ² cannot be negative or complex because of the way it is defined,integral be finite quantity



is the mathematical statement that the particle exists somewhere at all times.