Notes The hydrogen atom A hydrogen atom consists of proton and electron. The electron is orbiting round the nucleus and the nucleus also in general is in motion. So we assign coordinates for both ...

Notes Angular momentum operator in spherical coordinates The angular momentum operator in quantum mechanics is a crucial observable that represents the rotational motion of a particle. In spherical coordinates (r,θ,ϕ), the ...

Notes Energy Eigen values and normalized eigen function of free particle with box normalization In order to find the energy eigen values and normalized eigen functions we apply the method of Box with periodic boundary conditions.Consider two wave functions 𝜓(x) and u(x). The ...

Notes Square well with finite potential A square well potential with finite depth refers to a common model in quantum mechanics where a particle is confined within a potential well that has a rectangular shape.Let ...

Notes Uncertainty about the azimuthal angle for spherical harmonics We know that the components of the angular momentum operator (Lx, Ly, Lz) do not commute each other.Thus one cannot measure these components simultaneouslyHence the component of L ...

Notes Transmission coefficient for α particle emitted from the nucleus A radio isotope may decay into an α particle and a relaxed nucleus. Here we predict tunneling of an α particles through a coulomb potential barrier assuming free particle of ...

Notes Infinite square well potential The particle of mass m is in one dimensional infinite square well potential characterized byV(x) = 0 ; -L< x< L= ∞ ; l xl ≥ LThe ...

Notes Double well model of a molecule The double well model is a simplified representation used in quantum mechanics to describe certain molecular systems, particularly those with bistable potential energy surfaces. In this model, the …