Quantum Mechanics

Quantum Mechanical Wave Functions

I understand this mathematically but not conceptually, in terms of the Wave Equation

Expectation Value

The expectation value $⟨x⟩$ is the weight average of a given quantity. In general, the expect value of $x$ is

$$\text{For discrete possibilities: }⟨x⟩=\sum _i{P}_i{x}_i$$ $$\text{For infinite possibilities: }⟨x⟩=\int P(x)xdx=\int |\psi (x{)}^2|xdx=\int \psi (x{)}^{\ast }\psi (x)xdx$$

Note $P(x)=|\psi (x){|}^2$

For some function with infinite possibilities the expectation value is

$$⟨g(x)⟩=\int {\psi }^{\ast }(x)g(x)\psi (x)dx$$

See Dirac Notation

Uncertainty in Quantum Mechanics

• Classical measurement error
• Probabilistic quantities
• Uncertainty Principle
• Observer Effect
• State is usually unknown Note Einstein-Podolsky-Rosen Paradox

Conservation

Particle	Symbol	Lepton number ($L_e$)	Lepton number ($L_{\mu }$)	Lepton number ($L_{\tau }$)	Baryon number ($B$)	Strangeness number	Electric Charge
Electron	$e^{-}$	1	0	0	0	0	e
Electron Neutrino	${\nu }_e$	1	0	0	0	0	0
Muon	${\mu }^{-}$	0	1	0	0	0	-e
Muon Neutrino	${\nu }^{-}$	0	1	0	0	0	0
Tau	${\tau }^{-}$	0	0	1	0	0	-1
Tau Neutrino	${\nu }_{\tau }$	0	0	1	0	0	0
Negative Pion	${\pi }^{-}$	0	0	0	0	0	-e
Zero Pion	${\pi }^0$	0	0	0	0	0	0
Positive Pion	${\pi }^{+}$	0	0	0	0	0	e
Positive Kaon	$K^{+}$	0	0	0	0	1	e
Negative kaon	$K^{-}$	0	0	0	0	–1	-e
Proton	$p$	0	0	0	1	0	e
Neutron	$n$	0	0	0	1	0	0
Lambda zero	${\Lambda }^0$	0	0	0	1	–1	0
Positive Sigma	${\Sigma }^{+}$	0	0	0	1	–1	e
Negative sigma	${\Sigma }^{-}$	0	0	0	1	–1	-e
Xi zero	${\Xi }^0$	0	0	0	1	–2	0
Negative xi	${\Xi }^{-}$	0	0	0	1	–2	-e
NegativeOmega	${\Omega }^{-}$	0	0	0	1	–3	-e
Photon	$\gamma$	0	0	0	0	0	0

Baryon Conservation Lepton Conservation Strangeness

See also

Entanglement