Eigenfunctions Study guides, Class notes & Summaries

Contents 1 First-Order Differential Equations 1 1.1 Terminology and Separable Equations 1 1.2 The Linear First-Order Equation 12 1.3 Exact Equations 19 1.4 Homogeneous, Bernoulli and Riccati Equa tions 28 2 Second-Order Differential Equations 37 2.1 The Linear Second-Order Equation 37 2.2 The Constant Coefficient Homogeneous Equation 41 2.3 Particular Solutions of the Nonhomogeneous Equation 46 2.4 The Euler Differential Equation 53 2.5 Series Solutions 58 3 The Laplace Transform 69 3.1 Definiti...

These notes cover the concepts of boundary value problems and eigenfunctions, including the 3 cases one can come across. Several worked out examples problems are included. The material comes from the differential equations class taught by Peter Brady at Stevens Institute of Technology.

This document introduces to Sturm-Liouville eigenvalue problems, regular, singular and periodic, to find eigenvalues and eigenfunctions of partial differential equations. In introduces the concept of orthogonality of eigenfunctions. Then it focuses on how to generate the generalised Fourier series expansion of a function, and in particular the Fourier-Bessel and Fourier-Legendre series. Finally, it introduces inhomogeneous problems and how to solve them.

Concise collection of assignment questions on following topics in Quantum Mechanics-I. FAILURE OF CLASSICAL PHYSICS - blackbody radiation, atomic spectroscopy, photoelectric effect, Compton effect, de Broglie’s hypothesis, Davisson-Germer experiment, double slit experiment. WAVE STATE - Born interpretation and probability density, linear superposition, uncertainty principle, time-dependent and time-independent Schrodinger equation, free particle Gaussian, wavepackets and Fourier transform. ...

De aantekeningen van hoorcollege 2 van het vak From quantum to molecule. Het document bevat duidelijke afbeeldingen. Verder is het overzichtelijk en duidelijk gemarkeerd. Het is geschreven in het Engels met een paar Nederlandse aantekeningen.

Compilation of semester exam level questions in Quantum Mechanics-I on following topics. FAILURE OF CLASSICAL PHYSICS - blackbody radiation, atomic spectroscopy, photoelectric effect, Compton effect, de Broglie’s hypothesis, Davisson-Germer experiment, double slit experiment. WAVE STATE - Born interpretation and probability density, linear superposition, uncertainty principle, time-dependent and time-independent Schrodinger equation, free particle Gaussian, wavepackets and Fourier transform....

Compilation of semester exam level questions in Mathematical Physics-I on following topics. LINEAR ALGEBRA - linear vector spaces, metric and inner product spaces, function spaces, span and basis, orthonormal basis and transformation, Gram-Schmidt procedure, Schwarz inequality, Bessel inequality, linear operators, identity and inverse, commutators, adjoint, hermitian, skew-hermitian, unitary, and orthogonal operators, basis expansion, matrix representation of functions and operators, operator t...