Quantum mechanics lectures

vector - matrix - multiplying them







fundemental principles







in the next video , u will see


Discrete Energy Levels
 Electrons orbit their atomic nucleus in well defined orbits corresponding to discrete energy levels. The electrons can jump from one energy level to a vacant energy level, but they cannot exist in between. Transitions between these energy levels gives rise to absorption and emission of light in discrete spectral lines (wavelengths). The students are encouraged to look through their diffraction gratings at helium and neon light sources to see evidence of these discrete wavelengths of emitted light.

 Particles and Waves
 Quantum mechanics introduces some very non-intuitive concepts, e.g. light behaves as both a particle (a photon) and a wave, and a particle behaves like a wave with a wavelength inversely proportional to its momentum. Interference is a wave phenomenon, and indeed particles can interfere with each other. Both the position and momentum of a particle cannot be accurately specified at the same time (Heisenberg's uncertainty principle).

 Diffraction by a Slit

 Diffraction of light by a narrow vertical slit is a well understood classical wave phenomenon consistent with Heisenberg's uncertainty principle. The narrower the slit, the smaller is the uncertainty in the horizontal position of the photons which have to sneak through the narrow opening, so the greater is the horizontal spread of the transmitted protons (uncertainty in their momentum). Quantum mechanics only allows you to predict positions of particles with certain probabilities. In the classical, Newtonian, world you can predict the position and movement of a particle to any degree of accuracy - NOT in the microscopic quantum world. The Newtonian picture is perfect for describing the behaviour of basketballs and planets in the macroscopic world.                                                                                



let us return to classical mechanics and know something about vectors









then come back to quantum mechanics




 





 the identity of operator






 operator - matrix multiplication - example 1







operator - matrix multiplication - example 2





adjoint operator
 



Defination of hermitian operator


   


Hermitian Operators - Eigenvalues & Eigenvectors

 



Example Of Orthonormal Function




Unitary Operator





State Vector - General Concepts



POSITION OPERATOR- Dirac Delta Function



Momentum Operator - Hermitian Properties



THE BEST LECTURE I'VE EVER SEEN



Eigenfunctions of Momentum Operator






The Double Slit Experiment, Matter both a Particle and a Wave


Properties Of Dirac Delta Function


Fourier Transform Of Dirac Delta Function


Dirac Normalization Of Momentum Eigenfunctions - Part 1


Momentum And Position Commutator


Expectation value

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