Quantum Physics Part-1

Name: Quantum Physics Part-1
Rating: 3.8 (9 reviews)

Quantum Physics Part-1 for Undergraduate and Graduate Students and for GRE Physics exam.

Created bySubrahmanya L. Hegde

Last updated 3/2024

English

What you'll learn

Introduction and Understanding the 'Double Slit Experiment'.
1D Problems and Mathematical Formalism of Quantum Mechanics.
3D Problems, Angular Momentum, Spin, Time Independent Perturbation Theory etc.
Understanding the concepts and solving problems in each topics.

Course content

4 sections • 84 lectures • 78h 23m total length

Double Slit Experiment1:01:01
Big and Small44:34
Double Slit Experiment Continued36:09
During the continued double-slit experiment, electrons in a translation superposition state show interference when unobserved, but measuring which slit they pass through collapses the state and removes the interference.
Double Slit Experiment
Single Slit Diffraction and Uncertainty1:04:07
Schrodinger Equation56:26
Probability, Discrete and Continuous Distribution and Standard Deviation1:03:45
Basic Integrals (Optional)59:32
Infinite Integrals required for Quantum Physics44:45
Define and apply the gamma function through zero-to-infinity integrals, derive properties like gamma(n+1)=n!, and use substitutions to evaluate infinite integrals in quantum mechanics.
Wave Function and Interpretations1:17:57
Explore how the wave function provides probabilistic information, with |ψ|^2 as the position probability density, normalization to one, and measurement leading to collapse in identically prepared systems.
Normalization37:43
Operators in Quantum Mechanics58:42
Time Independent Schrodinger Equation and Stationary States1:31:37
Linear Combination State and Superposition State of Double Slit30:01
Explore linear combinations of energy states and the resulting superposition, and how measurements yield definite eigenvalues with probabilities. Discuss normalization, probability amplitudes, and the energy expectation value.
Differential Equations46:40
Linear Differential Equation With Constant Coefficient1:00:32
Fourier Series1:36:47
Fourier Series Problem and Complex Form29:54
Explore Fourier series representations of a piecewise function using sine, cosine, and the complex form; compute coefficients with integrals, examine convergence and discontinuities.
1D Box Derivation of Energy Eigenvalue and Eigenstate and Applicability58:15
1D Box : Properties of energy eigenstates and measurement1:17:39
1D Box : Symmetric Well and Stationary State Problems Hints53:01
1D Box : Measurement Born Interpretation40:46
Explore how a normalized wave function for a particle in a 1d box encodes probability amplitudes and how measurement collapses superpositions to energy eigenstates with probabilities given by squared amplitudes.
1D Box : Wall Moved Suddenly Measurement Problem41:25
Explore the sudden-wall expansion in a one-dimensional box, express the initial state in the final Hamiltonian basis, and compute energy probabilities for the ground and excited states.
1D Box : Linear Combination State Problems1:06:39
Explore how a particle in a one-dimensional box forms a linear combination of eigenstates. Apply normalization and probabilities to predict energy measurements and expected values.
LHO : Classical Part44:49
Explore how stable equilibrium yields small-amplitude simple harmonic motion via Taylor expansion of a general potential, and compare classical and quantum oscillator energy and origin shifts.
LHO : Ladder Operators and Finding Energy Eigenvalues and Eigenfunctions1:24:09
LHO : Raising and Lowering Operator Uses51:11
LHO : Problems Hints1:14:39
Explore the harmonic oscillator using ladder operators to derive energy eigenvalues and stationary states, compute expectation values and uncertainties, and analyze measurement outcomes and wave-function symmetry.
LHO : Problem Hints 244:21
Fourier Transform-1 : Definitions, Properties and a Problem59:51
Fourier Transform-2 : Problems34:40
Explore how to compute Fourier transforms through worked examples, exploring real integrals, even/odd function properties, and the relationship between time and frequency domains.
The Free Particle-149:07
The Free Particle-2 : Realization of Uncertainty Principle37:04
Free Particle-3 : Group and Phase Velocity50:04
Dirac Delta Properties44:54
Dirac Function Well54:29
Probability Current Density40:07
Bound and Scattering States55:06
Explore bound and scattering states by contrasting classical turning points and classically allowed regions with quantum tunneling, highlighting discrete versus continuous spectra across various potentials.
Step Potential1:02:48
Finite Potential Well1:21:39

Vectors and Linear Vector Space37:26
Linear Dependency and independency1:00:17
Explore the concepts of linear independence and dependence, bases and dimension in vector spaces, using polynomial and matrix examples to illustrate linear combinations.
Inner Product and Hilbert Space1:08:54
Hilbert Space Examples and Functional Space Etc57:00
Linear Operators and Hermitian Conjugation1:07:08
Explore linear operators and hermitian conjugation, including matrix representations, inner products, and the dagger adjoint in finite and infinite dimensional spaces and unitary or self-adjoint cases.
Eigen Value Eigen Vector; Theorems on Hermitian Operator Eigenvalues and Eigenve43:58
Projection Operator56:00
Projection operators in Hilbert and functional spaces are explained, showing how orthonormal bases, inner products, and coefficient expansions yield vector projections and eigenvalue insights.
Matrix Elements55:49
Determinants Matrices and Rank of Matrices1:02:55
Consistency of system of linear equations32:01
Matrix Eigenvalue Problems1:12:05
Caley Hamilton Theorem and Eigenvalue Problems45:30
Explore the Cayley-Hamilton theorem and eigenvalue problems, showing how to find eigenvalues and eigenvectors, handle degeneracy, and use the characteristic equation for diagonalization.
Degenerate Eigenvalues40:34
Diagonalization53:22
Powers and Functions of Operator (Matrix)40:31
Explore how to compute functions of matrices and operators using power series, diagonal matrices, and eigenvalues, enabling unitary time evolution and hamiltonian applications in quantum mechanics.
Diagonalizability16:03
Formalism-1 : Observables Determinate States and Eigenfunctions of Hermitian Op1:13:18
Formalism-2 : Continuous Spectra and Generalized Interpretation.mp41:14:16
Formalism-3 : Position Space and Momentum Space Wave Functions and Measurement49:47
Formalism-4 : Commutator Algebra57:28
Explore formalism of commutator algebra in quantum mechanics, defining operators and adjoints, evaluating commutators, and applying Jacobi identity to joint eigenstates and uncertainty relations.
Formalism-5 : Generalized Ehrenfest Theorem and Virial Theorem39:23
Generator of Translation in space and time16:26
Formalism Problems-11:01:56
Explore quantum formalism by defining Hilbert spaces of square-integrable functions on [0,1], and analyze linear operator combinations, adjoints, eigenvalues, sequential measurements, probabilities, and time evolution with a hamiltonian.
Formalism Problems-227:06
Measurement and Problems32:11
Solve only first problem in the video. Other problems can be solved after next section.
Time Evolution and Problems18:08
Solve only first two problem in the video. Other problems can be solved after next section.

3D Schrodinger Equation and Stationary and Linear Combination States21:54
2D 3D Box and Harmonic Oscillator1:11:07
Spherically Sym Potential1:05:17
H-Atom42:58
Angular momentum-1 (Orbital)1:03:12
Angular Momentum-2 : Ladder Operator Method1:10:35
Angular Momentum-3 : Generalization and Matrix Representation1:24:04
Generalize angular momentum from orbital motion to internal spin using matrix representations and ladder operators, deriving finite-dimensional J^2 and J_z eigenvalues.
Spin1:16:13
Spin Measurement24:04
Electron in External Magnetic Field1:08:49
Stern–Gerlach Experiment55:01
Spin Measurement Problems1:31:03

Requirements

Calculus
Basics of Linear Algebra
Basics of probability and statistics

Description

This course is undergraduate level Quantum Physics course that helps the students to understand basic concepts and applications. Course is helpful for solving standard textbook and to prepare for GRE Physics exam.

To overcome challenges of online learning, I am trying to implement a method in which online teacher and students refer the same textbooks. Whenever students gets doubts, teacher can tell the student to read particular page or paragraph of the book or suggest some problems from the book.

Learning Physics contains two major parts. First is to understand the concepts and mathematical structure of the theory. Second one is to apply them. So, most of the authors included lot of creative problems in their books along with the theory. While applying the concepts during problems, again we will again get to know the gaps in our understanding. Hence, solving more and more problems becomes major part of Learning Physics.

I might have solved many problems in the beginning of the course. Just watching the video lecture doesn't mean you could able to do those problems yourself. After each sessions, try to build theory and solve problems yourself without the help of book or video. Even you solve thousands of problems by looking into videos, solution manual etc. that doesn't count. Only thing that does matter is how many problems that you can do yourself. Take problems as challenge and solve.

Learning is not one way process. Students can ask doubts any time in this course. I will be very happy to answer.

Who this course is for:

College and University Physics Students
For those who wish to understand Quantum Computation and Quantum Information, this is the beginning.
Undergraduate Physics Students
Post Graduate Physics Students
For those who are preparing GRE Physics

Quantum Physics Part-1

What you'll learn

Explore related topics

Course content

1. Introduction39 lectures • 36hr 7min

Linear Algebra and Formalism26 lectures • 21hr

3D Problems, Angular Momentum and Spin12 lectures • 12hr 14min

Time Independent Perturbation Theory7 lectures • 9hr 3min

Requirements

Description

Who this course is for: