Quantum Mechanics II - (Lecture 2) - (The Linear Vector Space)

Описание: Prepared By: Muhammed A.Kareem


ئەم وانانە دەخوێندرێن لە قۆناغی سێیەمی بەشی فیزیا لە کۆلێژی زانستی زانکۆی سەڵاحەددین - هەولێر




Quantum Mechanics 1 Lectures - Asst. Prof. Dr. Mohammed Issa

   • Quantum Mechanics 1 Lectures - Dr. Mohamme...  


Quantum Mechanics 2 Lectures - Asst. Prof. Dr. Mohammed Issa

   • Quantum Mechanics 2 Lectures - Dr. Mohamme...  




Textbook :

Quantum Mechanics: Concepts and Applications -
by Noureddine Zettili





Chapter 2 : (Mathematical Tools of Quantum Mechanics)


2.1 Introduction
2.2 The Hilbert Space and Wave Functions
2.2.1 The Linear Vector Space
2.2.2 The Hilbert Space
2.2.3 Dimension and Basis of a Vector Space
2.2.4 Square-Integrable Functions: Wave Function
2.3 Dirac Notation
2.4 Operators
2.4.1 General Definitions
2.4.2 Hermitian Adjoint
2.4.3 Projection Operators
2.4.4 Commutator Algebra
2.4.5 Uncertainty Relation between Two Operators
2.4.6 Functions of Operators
2.4.7 Inverse and Unitary Operators
2.4.8 Eigenvalues and Eigenvectors of an Operator
2.4.9 Infinitesimal and Finite Unitary Transformations
2.5 Representation in Discrete Bases
2.5.1 Matrix Representation of Kets, Bras, and Operators
2.5.2 Change of Bases and Unitary Transformations
2.5.3 Matrix Representation of the Eigenvalue Problem
2.6 Representation in Continuous Bases
2.6.1 General Treatment
2.6.2 Position Representation
2.6.3 Momentum Representation
2.6.4 Connecting the Position and Momentum Representations
2.6.5 Parity Operator
2.7 Matrix and Wave Mechanics
2.7.1 Matrix Mechanics
2.7.2 Wave Mechanics
2.8 Concluding Remarks
2.9 Solved Problems
2.10 Exercises







In this chapter we introduce the essential mathematical tools required for the formulation and understanding of quantum mechanics. Since quantum theory is inherently mathematical, a solid grasp of linear algebra, complex vector spaces, operators, and eigenvalue problems is indispensable. These tools provide the language in which quantum states, observables, and physical measurements are described. The purpose of this chapter is not merely to present mathematical techniques, but to establish the mathematical framework that underlies the postulates of quantum mechanics and will be repeatedly used throughout the development of the theory.











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