Modern Physics

 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

 Pauli's Exclusion Principle; Pauli found that in a quantum mechanical system, no two electrons can occupy the same state, i.e no two electrons can have the same set of quantum number n,l,mₗ and mₛ. With the help of this principle, one can explain the construction of the periodic table. Let us consider a system of two non-interacting identical particles. Let the particle 1 be in a quantum state denoted by a, so that its wavefunction is  Also, the particle 2 is in quantum state b so that its wavefunction is  The total wavefunction is given by When the particles are exchanged then the total wavefunction is given by We have two types of the wavefunctions for a system of two particles. Symmetric and Antisymmetric Wavefunction; Now the wavefunction which do not change sign on exchange of particles are called symmetric wavefunction and those which change their sign on exchange of particles are called anti-symmetric wavefunction. Symmetric wavefunction: For a symmetric wavefunction The li

Quantum numbers(n,l,m) Hydrogen atom is spherical symmetric. The Schrodinger equation in spherical polar coordinates can be separated by three independent equations,each giving rise to a quantum number n,l and mₗ, the physical significance of these number is explained as follows. Quantum number 'n' (Principal quantum number). The quantum number 'n' is called the principal quantum number (or radial) quantum number. It can have only positive integral values 1,2,3,......n. The principal quantum number defines the total energy of the electron in the orbit. Eₙ ∝ 1/n² Quantum number 'l' (orbital quantum number). The quantum number 'l' is the orbital quantum number. It defines the orbital angular momentum of the electron given by Orbital angular momentum. It can have only positive integral values 0,1,2,.....(n-1). For example, for n=3, the possible values of l are 0,1,2, only. Quantum number mₗ (magnetic quantum number) The magnetic quantum number decides the Z

 Quantum Tunnelling; Quantum Tunnelling. Quantum Tunnelling.

 Particle in a potential barrier; Particle in a potential barrier. Particle in a potential barrier.

 Finite potential well; Particle in finite potential well. Particle in finite potential well. Particle in finite potential well.

 Particle in one dimensional box/Infinite square potential well. Particle in one dimensional box. Infinite square potential well.