Linear Transformations

Vector Spaces and Linear Transformations

Transformations or Mappings, Group Homomorphism and Isomorphism, Linear Transformations on Vector Spaces, Non-singular Transformations, Vector Space Isomorphism.

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Algebra and Matrix Representations of Linear Transformations

Operations on Linear Transformations, Operations on Linear Operators, Algebra of Linear Transformations, Representation of Linear Transformations by Matrices.

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Linear Operators in Quantum Mechanics

Space of Wave Functions, Hermitian and Anti Hermitian Operators, Expectation Value and Uncertainty, Eigenvalues and Eigenvectors, Degeneracy.

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Reference:

• S P Kuila, ``Vector Analysis, Tensor Analysis and Linear Vector Space"
• B.S. Vatssa, ``Elements of Modern Algebra"
• Arfken and Weber, "Mathematical Methods for Physicists"
• S Lipschutz, ``Schaum's Outlines: Linear Algebra"

Atanu Kumar

Assistant Professor

Department of Physics

Chandernagore College

atanukum@gmail.com

Some Special Integrals

Topics Covered:

Beta  and Gamma Functions  and  Relation between  them. Expression  of  Integrals in terms  of  Gamma Functions.  Error  Function  (Probability  Integral).

Target Audience: 

3rd Semester Physics Honours Students of Chandernagore College

Class-notes Download Link: 

Some Special Integrals

Lectures:

Part I

Part II

Part III

Reference:

• Arfken and Weber, "Mathematical Methods for Physicists"
• D Biswas, "Mathematical Methods in Physics"

Atanu Kumar

Assistant Professor

Department of Physics

Chandernagore College

atanukum@gmail.com