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Basic Concepts of Quantum Mechanics

Nov 12, 2018
15 minutes read

Some basic concepts for Quantum Mechanics.

Quantum-Mechanics

Preliminary Mathematics

Nov 5, 2018
14 minutes read

The preliminary Mathematical knowledge for Quantum Field Theory. Containing the Minkowski Spacetime, Lorentz Group, and the representation theory of Lorentz Group.

Jan 1, 0001
12 minutes read

Random Variable Introduction to Probability Theory Probability Space [Definition] : A Probability Space is a triplet

(Ω, F, P)

of three elements:

Ω

is a set (called Sample Space) .

F

is a Sigma Algebra on

Ω

F

is a collection of subsets of

Ω

and has the following properties:

Ω, \emptyset \in F

A \in F \Rightarrow A^{c} \equiv Ω ∖ A \in F

A sequence of sets

A_{i} {i = 1}^{\infty}

A_{i} \in F

⋃ {j = 1}^{\infty} A_{j} \in F

P

is a Probability Measure:

P : F \to [0, 1]

and has the following properties: (Normalization)

P (Ω) = 1

(Countably additive)

A_{1}, A_{2}, \dots \in F, A_{i} ⋂ A_{j} = \emptyset \Rightarrow P (⋃_{j = 1}^{\infty} A_{j}) = \sum_{j = 1}^{\infty} P (A_{j})

[Definition] : A Measurable (real-valued) Function on a Measurable Space

(Ω, F)

f : Ω \to R

, which has the property:......