Quantum Chemistry

2.

Fundamental Postulates of Quantum Mechanics

2.1.

Postulate I: State Description

2.1.1.

The Wavefunction

2.1.1.1.

Mathematical Properties

2.1.1.2.

Continuity Requirements

2.1.1.3.

Single-Valuedness

2.1.1.4.

Square Integrability

2.1.2.

Born Interpretation

2.1.2.1.

Probability Density

2.1.2.2.

Probability Current

2.1.2.3.

Statistical Nature of Quantum Mechanics

2.1.3.

2.1.3.1.

Normalization Condition

2.1.3.2.

Normalization Constant

2.1.3.3.

Physical Significance

2.2.

Postulate II: Observable Representation

2.2.1.

Quantum Mechanical Operators

2.2.1.1.

Correspondence Principle

2.2.1.2.

Classical to Quantum Mapping

2.2.2.

Fundamental Operators

2.2.2.1.

Position Operator

2.2.2.2.

Momentum Operator

2.2.2.3.

Angular Momentum Operators

2.2.2.4.

Hamiltonian Operator

2.2.3.

Operator Properties

2.2.3.1.

2.2.3.2.

2.2.3.3.

Commutation Relations

2.3.

Postulate III: Measurement Process

2.3.1.

Eigenvalue Equation

2.3.1.1.

Observable Eigenvalues

2.3.1.2.

Measurement Outcomes

2.3.1.3.

Eigenfunctions as States

2.3.2.

Expectation Values

2.3.2.1.

Definition and Calculation

2.3.2.2.

Physical Interpretation

2.3.2.3.

Time Dependence

2.3.3.

Probability of Measurement Outcomes

2.3.3.1.

Expansion in Eigenfunctions

2.3.3.2.

2.4.

Postulate IV: Time Evolution

2.4.1.

Time-Dependent Schrödinger Equation

2.4.1.1.

2.4.1.2.

Unitary Time Evolution

2.4.1.3.

Conservation Laws

2.4.2.

Time Evolution Operator

2.4.2.1.

Relationship to Hamiltonian

2.5.

Postulate V: Stationary States

2.5.1.

Time-Independent Schrödinger Equation

2.5.1.1.

Separation of Variables

2.5.1.2.

Stationary States

2.5.1.3.

Energy Eigenvalue Problem

2.5.2.

Superposition Principle

2.5.2.1.

Linear Combinations

2.5.2.2.

Interference Effects

2.5.2.3.

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1. Introduction to Quantum Chemistry

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3. Exactly Solvable Quantum Systems