Notes Precession of an electron in magnetic field We consider an electron which has only spin degree of freedom. The electron has spin. The electron is negatively charged particle. So it has magnetic moment 𝜇_s due to spin. ...

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 Charged oscillator in an electric field In quantum mechanics, the behaviour of a charged oscillator in an electric field can be described using the Schrödinger equationF = qeF = - dV/ dXdv = ...

Notes Projection operator onto q dimensional subspace 𝜖q The projection operator onto a q-dimensional subspace in quantum mechanics is a mathematical tool used to isolate a specific subspace within a larger quantum system. Let's break down this concept:...

Notes Significance of a+ and a In quantum mechanics, "a+" and "a" are operators that are used to describe the behaviour of a quantum system, like the magical bouncing ball we talked about earlier. They're like ...

Notes Comparison of classical and quantum probability density of harmonic oscillator The comparison between classical and quantum probability density of a harmonic oscillator highlights some fundamental differences between classical mechanics and quantum mechanics. The harmonic …

Notes The Coherent states The eigen states of annihilation operator are known as coherent states.The normalized ket ∣α⟩ represents a quantum state in quantum mechanics. It's often used to describe a ...

Notes Harmonic oscillator problem by matrix method Matrix Representation: Represent the Hamiltonian operator as a matrix in a finite-dimensional basis. You need to choose an appropriate basis, often involving position or momentum states, and …