Operators.

Operators:

Operator is a rule or set of rules which when applied to a function within a given domain produces another function within a given range.

For example, when differential operator is applied to a function f(x) it changes into another function g(x) within a given range.

In quantum mechanics, since the momentum and energy cannot be measured accurately due to uncertainty principle. The operator are important to find the average or expectation values of energy, momentum etc. The various operators are given below.

1) Energy operator.

2) Momentum operator.

3) kinetic energy operator.

4) Hamiltonian operator.

5) Angular momentum operator.

Different operators.

Comments

Mass defect, packing fraction and binding energy.

Mass defect, packing fraction and binding energy: It was assumed that mass of the nucleus is equal to the mass of its constituents (i.e protons and neutrons). But experimentally it was found that the actual mass of the nucleus is less than the theoretical mass. Thus, the difference between the theoretical mass and experimental mass is called mass defect i.e ∆m={[Zmₚ + (A-Z)mₙ] - M} Where mₚ= mass of proton mₙ= mass of neutron M= actual mass of nucleus Z= atomic number A= mass number The ratio of mass defect and mass number (A) is called packing fraction (f) f = ∆m/A Thus packing fraction is the mass defect available per nucleon. The packing fraction explains the stability of the nucleus. The packing fraction may be positive, negative or zero. The positive value of packing fract...

Different kinds of beta decay.

Different kinds of beta decay 1) Negative beta decay process: When there is excess number of neutrons in the nucleus, the neutron is converted into proton with the emission of electron and antineutrino particle and this process is called negative beta decay process. Negative beta decay. 2) Positive beta decay process: When there is excess number of protons in the nucleus, the proton is converted into neutron with the emission of positron and neutrino particle and this process is called positive beta decay process. Positive beta decay. 3) Electron Capture: When there is excess number of protons in the nucleus, sometimes the nucleus will absorbed the nearby electrons in the nearest electron orbital emitting neutron and a neutrino and this process is called electron capture. Electron capture. 4) Inverse beta decay: Inverse beta decay. Thus such kind of reaction in which neutrinos are absorbed to create some sort of beta decay is called inverse beta decay. Inverse beta decay confirm t...

LS coupling and jj coupling.

Total angular momentum: The total angular momentum of an electron is the sum of the orbital angular momentum and spin angular momentum of the electron i.e Coupling Scheme Since an atom consist of large number of electrons having different orbital and spin momenta, Coupling scheme is necessary to obtain the resultant orbit and spin momenta of atom as a whole. There are two types of coupling scheme namely 1) LS Coupling 2) JJ Coupling. 1)LS Coupling: In this coupling the 'l' vectors of all electrons combine to form resultant 'L' vector and all the 's' vectors of these electrons combine to form resultant 'S' vector. Then the 'L' vector and 'S' vector undergoes vector addition to give resultant 'J' vector which represents the total angular momentum of an atom. Symbolically LS coupling is represented as This type of coupling is governed by the following principles: 1) All the three vectors (L,S and J vectors) are quantized. 2)L is an ...

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