Benutzer:Troyaner/Physics

Physik

Relativitätstheorie

$u_{x}={\frac {u_{x}'+v}{1+{\frac {u_{x}'v}{c^{2}}}}},\quad u_{y}={\frac {u_{y}'{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}{1+{\frac {u_{x}'v}{c^{2}}}}},\quad u_{z}={\frac {u_{z}'{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}{1+{\frac {u_{x}'v}{c^{2}}}}}$

$u_{x}'={\frac {u_{x}-v}{1-{\frac {u_{x}v}{c^{2}}}}},\quad u_{y}'={\frac {u_{y}}{{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}(1-{\frac {u_{x}v}{c^{2}}})}},\quad u_{z}'={\frac {u_{z}}{{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}(1-{\frac {u_{x}v}{c^{2}}})}}$

$\Delta t'={\frac {\Delta t}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}$

$\Delta t'=\gamma \Delta t$

Größen und Einheiten der Mechanik

Größe	Formelzeichen	Name der Einheit	Einheitenzeichen	Beziehung zwischen den Einheiten
Arbeit, Energie	$W,E$	Joule	$J$	$1\mathrm {J} =1\mathrm {N} \cdot \mathrm {m} =1{\frac {\mathrm {kg} \cdot \mathrm {m} ^{2}}{\mathrm {s} ^{2}}}$
Beschleunigung	$\alpha$	Meter durch Quadratsekunde	${\frac {\mathrm {m} }{\mathrm {s} ^{2}}}$
Dichte	$\rho$	Masse (Kilogramm) geteilt durch Volumen (Kubikmeter)	${\frac {\mathrm {kg} }{\mathrm {m} ^{3}}}$	$1{\frac {\mathrm {kg} }{\mathrm {m} ^{3}}}=0,001{\frac {\mathrm {g} }{\mathrm {cm} ^{3}}}$
Drehimpuls	L	Newtonmetersekunde	N · m · s	1 N · m · s = 1 kg · m2 / s
Drehmoment	M	Newtonmeter	N · m	1 N · m = 1 kg · m2 / s2
Druck	p	Pascal	Pa	1 Pa = 1 N / m2 = 1 kg / m · s2
Drehzahl	n	durch Sekunde	1 / s	1 / s = 60 1 / min
Federkonstante	D, k	Newton durch Meter	N / m	1 N / m = 1 kg / s2
Fläche, Flächeninhalt	A	Quadratmeter	m2	1 m2 = 1 m · 1 m
Frequenz	f, v	Hertz	Hz	1 Hz = 1 / s
Geschwindigkeit	v	Meter durch Sekunde	m / s
Impuls	p	Kilogrammmeter durch Sekunde	kg · m / s	1 kg · m / s = 1 N · s
Kraft	F	Newton	N	1 N = 1 kg · m / s2
Länge	l	Meter	m	Basiseinheit
Leistung, Energiestrom	P	Watt	W	1 W = 1 J / s = 1 N · m / s = 1 kg · m2 / s3
Masse	m	Kilogramm	kg	Basiseinheit
Schwingungsdauer, Periodendauer	T	Sekunde	s
Trägheitsmoment	J	Kilogramm mal Quadratmeter	kg · m2
Volumen	V	Kubikmeter	m3	1 m3 = 1m · 1m · 1m
Wellenlänge	λ	Meter	m
Winkelbeschleunigung	α	Radiant durch Qaudratsekunde	rad / s2	1 rad / s2 = 1 / s2
Winkelgeschwindigkeit	ω	Radiant durch Sekunde	rad / s	1 rad / s = 1 / s
Zeit	t	Sekunde	s<b	Basiseinheit

Naturkonstanten-Tabelle

Bezeichnung der Konstante	Symbol(e)	Wert
Elektromagnetismus
Coulomb-Konstante	k = 1/(4πε0)	(22 468 879 468 420 441 / 2 500 000) m F−1 ≈ 8,987 551 787 37 · 109 m F−1
Curie-Konstante		stoffspezifisch
Dielektrizitätskonstante des Vakuums	ε0 = 1/(μ0c02)	625 000 / (22 468 879 468 420 441 π) F m−1 ≈ 8,854 187 817 62 · 10−12 F m−1 (abgeleitet)
Elementarladung	e	1,602 176 53 (14) · 10−19 C
Hall-Widerstand	RK = h/e2	25 812,807 Ω
Lichtgeschwindigkeit (Vakuum)	c0, c	299 792 458 m s−1 (definiert)
Permeabilität des Vakuums	μ0	4π · 10−7 H m−1 (definiert) ≈ 12,566 370 614 · 10−7 T2 m3 J−1
Verdet-Konstante		stoffspezifisch, wellenlängenabhängig
Gravitation
Gravitationskonstante	G	6,674 2 (10) · 10−11 · m3 / (kg · s2)
Thermodynamik
Absoluter Nullpunkt	T0	−273,15 °C = 0 K (definiert)
Avogadro-Konstante	NA	6,022 141 5 (10) · 1023 mol−1
Boltzmann-Konstante	kB	1,380 650 5 (24) · 10−23 J K−1
		8,617 342 (15) · 10−5 eV K−1
Loschmidt-Konstante	L, NL	2,686 777 3 (47) · 1025 m−3 (bei: 273,15 K und 101,325 kPa)
Molvolumen eines idealen Gases, p = 1 bar, θ = 0 °C		22,413 996 (39) dm3 mol−1
Standard-Atmosphärendruck	atm	101,325 kPa (definiert)
Stefan-Boltzmann-Konstante	σ	5,670 400 (40) · 10−8 W m−2 K−4
Universelle Gaskonstante	R0 = NAkB	8,314 472 (15) J K−1 mol−1
Teilchenphysik
1. (Erste) Strahlungskonstante	c1	3,741 771 38 (64) · 10−16 Wm2
2. (Zweite) Strahlungskonstante	c2	1,438 775 2 (25) · 10−2 mK
Bohrscher Radius	a0 = 4π ε0 ħ2 / (me e2)	0,529 177 210 8 (18) · 10−10 m
Bohrsches Magneton	μB = e ħ / (2 me)	9,274 009 49 (80) · 10−24 J T−1
Plancksches Wirkungsquantum	h	6,626 069 3 (11) · 10−34 J s
		4,135 667 27 (52) · 10−15 eV s
	ħ = h/(2π)	1,054 571 596 (82) · 10−34 J s
Elektron
* Gyromagnetisches Verhältnis des freien Elektrons	γe	1,760 859 74 (15) · 1011 s−1 T−1
* Klassischer Elektronenradius	re	2,817 940 325 (28) · 10−15 m
* Landé-Faktor des freien Elektrons	ge	2,002 319 304 371 8 (75)
* Magnetisches Moment	μe	−9,284 764 12 (80) · 10−24 JT−1
* Molekulargewicht	Me	5,49 · 10−4
* Ruhemasse	me	9,109 382 6 (16) · 10−31 kg
* Spezifische Ladung	e/me	1,758 820 12 (15) · 1011 C kg−1
Feinstruktur-Konstante	α = μ0 e2 c0 / (2 h)	7,297 352 568 (24) · 10−3
	α−1	137,035 999 11 (46)
Neutron
* relative Atommasse	n	1,008 664 915 60 (55)
* Ruhemasse	mn	1,674 927 28 (29) · 10−27 kg
Nukleares Magneton, Kern-Magneton	μN = e ħ / (2 mp)	5,050 786 6 (17) · 10−27 J T−1
Proton
* Gyromagnetisches Verhältnis	γp	2,675 222 05 (23) · 108 s−1T−1
* Magnetisches Moment	μp	1,410 606 71 (12) · 10−26 JT−1
* Magnetisches Moment in H2O	μ’p/μB	1,520 993 132 (16) · 10−3
* Resonanzfrequenz per Feld in H2O	γ'p/2π	42,576 375 (13) MHzT−1
* Ruhemasse	mp	1,672 621 71 (29) · 10−27 kg
Rydberg-Energie	R∞ch	13,605 141 384 3 (13) eV
Rydberg-Frequenz	R∞c	3,289 841 960 360 · 1015 s−1
Rydberg-Konstante	R∞ = e4 me / (8 ε02 h3 c)	1,097 373 156 852 5 (73) · 107 m−1
Verhältnis von Protonen- zu Elektronenmasse	mp/me	1 836,152 672 61 (85)
Vermischtes
Atomare Masseneinheit	mu, amu, u (g · NA−1)	1,660 538 86 (28) · 10−27 kg
Faraday-Konstante	F (e · NA)	96 485,338 3 (83) C Mol−1
(Gregorianisches) Jahr	a	365,242 5 d (definiert)
Hartree-Energie	Eh	4,359 748 2 (26) · 10−18 J
Magnetisches Flussquantum	Φ0 = h/(2e)	2,067 833 72 (18) · 10−15 Wb

Wichtige Funktionswerte

Winkel $\alpha$ (Grad)	$0^{\circ }$	$30^{\circ }$	$45^{\circ }$	$60^{\circ }$	$90^{\circ }$	$180^{\circ }$	$270^{\circ }$
Bogenmaß	$0\pi$	${\frac {\pi }{6}}$	${\frac {\pi }{4}}$	${\frac {\pi }{3}}$	${\frac {\pi }{2}}$	$\pi$	${\frac {3\pi }{2}}$
Sinus	$0\,$	${\frac {1}{2}}$	${\frac {1}{2}}{\sqrt {2}}$	${\frac {1}{2}}{\sqrt {3}}$	$1\,$	$0\,$	$-1\,$
Kosinus	$1\,$	${\frac {1}{2}}{\sqrt {3}}$	${\frac {1}{2}}{\sqrt {2}}$	${\frac {1}{2}}$	$0\,$	$-1\,$	$0\,$
Tangens	$0\,$	${\frac {1}{3}}{\sqrt {3}}$	$1\,$	${\sqrt {3}}$	-	$0\,$	-

Trigonometrie

Exp

$\sin(z)={\frac {e^{iz}-e^{-iz}}{2i}}$     $\sinh(z)={\frac {e^{z}-e^{-z}}{2}}$

$\cos(z)={\frac {e^{iz}+e^{-iz}}{2}}$     $\cosh(z)={\frac {e^{z}+e^{-z}}{2}}$

Reihenentwicklung

${\begin{aligned}\sin(z)&=z-{\frac {z^{3}}{3!}}+{\frac {z^{5}}{5!}}-{\frac {z^{7}}{7!}}+\dots =\sum _{n=0}^{\infty }(-1)^{n}{\frac {z^{2n+1}}{(2n+1)!}}\\\sinh(z)&=z+{\frac {z^{3}}{3!}}+{\frac {z^{5}}{5!}}+{\frac {z^{7}}{7!}}+\dots =\sum _{n=0}^{\infty }{\frac {z^{2n+1}}{(2n+1)!}}\\\cos(z)&=1-{\frac {z^{2}}{2!}}+{\frac {z^{4}}{4!}}-{\frac {z^{6}}{6!}}+\dots =\sum _{n=0}^{\infty }(-1)^{n}{\frac {z^{2n}}{(2n)!}}\\\cosh(z)&=1+{\frac {z^{2}}{2!}}+{\frac {z^{4}}{4!}}+{\frac {z^{6}}{6!}}+\dots =\sum _{n=0}^{\infty }{\frac {z^{2n}}{(2n)!}}\end{aligned}}$

Produktentwicklung

$\sin x=x\prod _{k=1}^{\infty }\left(1-{\frac {x^{2}}{k^{2}\pi ^{2}}}\right)$

$\cos x=\prod _{k=1}^{\infty }\left(1-{\frac {4x^{2}}{(2k-1)^{2}\pi ^{2}}}\right)$

Gleichungen

$\sin x=\pm {\sqrt {1-\cos ^{2}x}}={\frac {\pm \tan x}{\sqrt {1+\tan ^{2}x}}}$

$\cos x=\pm {\sqrt {1-\sin ^{2}x}}={\frac {\pm 1}{\sqrt {1+\tan ^{2}x}}}$

$\tan x={\frac {\pm {\sqrt {1-\cos ^{2}x}}}{\cos x}}={\frac {\pm \sin x}{\sqrt {1-\sin ^{2}x}}}$

Additionstheoreme

${\begin{matrix}\sin(x\pm y)&=&\sin(x)\cos(y)\pm \cos(x)\sin(y)\\\cos(x\pm y)&=&\cos(x)\cos(y)\mp \sin(x)\sin(y)\\\tan(x\pm y)&=&\displaystyle {\frac {\tan(x)\pm \tan(y)}{1\mp \tan(x)\tan(y)}}\\\\\end{matrix}}$

$\sinh(x\pm y)=\sinh(x)\cosh(y)\pm \cosh(x)\sinh(y)$

$\cosh(x\pm y)=\cosh(x)\cosh(y)\pm \sinh(x)\sinh(y)$

$\tanh(x\pm y)={\frac {\tanh(x)\pm \tanh(y)}{1\pm \tanh(x)\tanh(y)}}$

Vektoranalysis

Tabelle mit Nabla-Operator in Zylinder und Kugelkoordinaten

Operation	Kartesische Koordinaten (x,y,z)	Zylinderkoordinaten (ρ,φ,z)	Kugelkoordinaten (r,θ,φ)
Definition der Koordinaten		$\left[{\begin{matrix}x&=&\rho \cos \phi \\y&=&\rho \sin \phi \\z&=&z\end{matrix}}\right.$	$\left[{\begin{matrix}x&=&r\sin \theta \cos \phi \\y&=&r\sin \theta \sin \phi \\z&=&r\cos \theta \end{matrix}}\right.$
		$\left[{\begin{matrix}\rho &=&{\sqrt {x^{2}+y^{2}}}\\\phi &=&\operatorname {atan2} (y,x)\\z&=&z\end{matrix}}\right.$	$\left[{\begin{matrix}r&=&{\sqrt {x^{2}+y^{2}+z^{2}}}\\\theta &=&\arccos(z/r)\\\phi &=&\operatorname {atan2} (y,x)\end{matrix}}\right.$
$\mathbf {A}$	$A_{x}\mathbf {\hat {x}} +A_{y}\mathbf {\hat {y}} +A_{z}\mathbf {\hat {z}}$	$A_{\rho }{\boldsymbol {\hat {\rho }}}+A_{\phi }{\boldsymbol {\hat {\phi }}}+A_{z}{\boldsymbol {\hat {z}}}$	$A_{r}{\boldsymbol {\hat {r}}}+A_{\theta }{\boldsymbol {\hat {\theta }}}+A_{\phi }{\boldsymbol {\hat {\phi }}}$
$\nabla f$	${\partial f \over \partial x}\mathbf {\hat {x}} +{\partial f \over \partial y}\mathbf {\hat {y}} +{\partial f \over \partial z}\mathbf {\hat {z}}$	${\partial f \over \partial \rho }{\boldsymbol {\hat {\rho }}}+{1 \over \rho }{\partial f \over \partial \phi }{\boldsymbol {\hat {\phi }}}+{\partial f \over \partial z}{\boldsymbol {\hat {z}}}$	${\partial f \over \partial r}{\boldsymbol {\hat {r}}}+{1 \over r}{\partial f \over \partial \theta }{\boldsymbol {\hat {\theta }}}+{1 \over r\sin \theta }{\partial f \over \partial \phi }{\boldsymbol {\hat {\phi }}}$
$\nabla \cdot \mathbf {A}$	${\partial A_{x} \over \partial x}+{\partial A_{y} \over \partial y}+{\partial A_{z} \over \partial z}$	${1 \over \rho }{\partial (\rho A_{\rho }) \over \partial \rho }+{1 \over \rho }{\partial A_{\phi } \over \partial \phi }+{\partial A_{z} \over \partial z}$	${1 \over r^{2}}{\partial (r^{2}A_{r}) \over \partial r}+{1 \over r\sin \theta }{\partial \over \partial \theta }(A_{\theta }\sin \theta )+{1 \over r\sin \theta }{\partial A_{\phi } \over \partial \phi }$
$\nabla \times \mathbf {A}$	${\begin{matrix}({\partial A_{z} \over \partial y}-{\partial A_{y} \over \partial z})\mathbf {\hat {x}} &+\\({\partial A_{x} \over \partial z}-{\partial A_{z} \over \partial x})\mathbf {\hat {y}} &+\\({\partial A_{y} \over \partial x}-{\partial A_{x} \over \partial y})\mathbf {\hat {z}} &\ \end{matrix}}$	${\begin{matrix}({1 \over \rho }{\partial A_{z} \over \partial \phi }-{\partial A_{\phi } \over \partial z}){\boldsymbol {\hat {\rho }}}&+\\({\partial A_{\rho } \over \partial z}-{\partial A_{z} \over \partial \rho }){\boldsymbol {\hat {\phi }}}&+\\{1 \over \rho }({\partial (\rho A_{\phi }) \over \partial \rho }-{\partial A_{\rho } \over \partial \phi }){\boldsymbol {\hat {z}}}&\ \end{matrix}}$	${\begin{matrix}{1 \over r\sin \theta }({\partial \over \partial \theta }(A_{\phi }\sin \theta )-{\partial A_{\theta } \over \partial \phi }){\boldsymbol {\hat {r}}}&+\\{1 \over r}({1 \over \sin \theta }{\partial A_{r} \over \partial \phi }-{\partial \over \partial r}(rA_{\phi })){\boldsymbol {\hat {\theta }}}&+\\{1 \over r}({\partial \over \partial r}(rA_{\theta })-{\partial A_{r} \over \partial \theta }){\boldsymbol {\hat {\phi }}}&\ \end{matrix}}$
$\Delta f=\nabla ^{2}f$	${\partial ^{2}f \over \partial x^{2}}+{\partial ^{2}f \over \partial y^{2}}+{\partial ^{2}f \over \partial z^{2}}$	${1 \over \rho }{\partial \over \partial \rho }(\rho {\partial f \over \partial \rho })+{1 \over \rho ^{2}}{\partial ^{2}f \over \partial \phi ^{2}}+{\partial ^{2}f \over \partial z^{2}}$	${1 \over r^{2}}{\partial \over \partial r}(r^{2}{\partial f \over \partial r})+{1 \over r^{2}\sin \theta }{\partial \over \partial \theta }(\sin \theta {\partial f \over \partial \theta })+{1 \over r^{2}\sin ^{2}\theta }{\partial ^{2}f \over \partial \phi ^{2}}$
$\Delta \mathbf {A} =\nabla ^{2}\mathbf {A}$	$\Delta A_{x}\mathbf {\hat {x}} +\Delta A_{y}\mathbf {\hat {y}} +\Delta A_{z}\mathbf {\hat {z}}$	${\begin{matrix}(\Delta A_{\rho }-{A_{\rho } \over \rho ^{2}}-{2 \over \rho ^{2}}{\partial A_{\phi } \over \partial \phi }){\boldsymbol {\hat {\rho }}}&+\\(\Delta A_{\phi }-{A_{\phi } \over \rho ^{2}}+{2 \over \rho ^{2}}{\partial A_{\rho } \over \partial \phi }){\boldsymbol {\hat {\phi }}}&+\\(\Delta A_{z}){\boldsymbol {\hat {z}}}&\ \end{matrix}}$	${\begin{matrix}(\Delta A_{r}-{2A_{r} \over r^{2}}-{2A_{\theta }\cos \theta \over r^{2}\sin \theta }-{2 \over r^{2}}{\partial A_{\theta } \over \partial \theta }-{2 \over r^{2}\sin \theta }{\partial A_{\phi } \over \partial \phi }){\boldsymbol {\hat {r}}}&+\\(\Delta A_{\theta }-{A_{\theta } \over r^{2}\sin ^{2}\theta }+{2 \over r^{2}}{\partial A_{r} \over \partial \theta }-{2\cos \theta \over r^{2}\sin ^{2}\theta }{\partial A_{\phi } \over \partial \phi }){\boldsymbol {\hat {\theta }}}&+\\(\Delta A_{\phi }-{A_{\phi } \over r^{2}\sin ^{2}\theta }+{2 \over r^{2}\sin ^{2}\theta }{\partial A_{r} \over \partial \phi }+{2\cos \theta \over r^{2}\sin ^{2}\theta }{\partial A_{\theta } \over \partial \phi }){\boldsymbol {\hat {\phi }}}&\end{matrix}}$
infinitisimale Verschiebung	$d\mathbf {l} =dx\mathbf {\hat {x}} +dy\mathbf {\hat {y}} +dz\mathbf {\hat {z}}$	$d\mathbf {l} =d\rho {\boldsymbol {\hat {\rho }}}+\rho d\phi {\boldsymbol {\hat {\phi }}}+dz{\boldsymbol {\hat {z}}}$	$d\mathbf {l} =dr\mathbf {\hat {r}} +rd\theta {\boldsymbol {\hat {\theta }}}+r\sin \theta d\phi {\boldsymbol {\hat {\phi }}}$
infinitisimales Flächenelement	${\begin{matrix}d\mathbf {A} =&dydz\mathbf {\hat {x}} +\\&dxdz\mathbf {\hat {y}} +\\&dxdy\mathbf {\hat {z}} \end{matrix}}$	${\begin{matrix}d\mathbf {A} =&\rho d\phi dz{\boldsymbol {\hat {\rho }}}+\\&d\rho dz{\boldsymbol {\hat {\phi }}}+\\&\rho d\rho d\phi \mathbf {\hat {z}} \end{matrix}}$	${\begin{matrix}d\mathbf {A} =&r^{2}\sin \theta d\theta d\phi \mathbf {\hat {r}} +\\&r\sin \theta drd\phi {\boldsymbol {\hat {\theta }}}+\\&rdrd\theta {\boldsymbol {\hat {\phi }}}\end{matrix}}$
infinitisimales Volumenelement	$dV=dxdydz\,$	$dV=\rho d\rho d\phi dz\,$	$dV=r^{2}\sin \theta drd\theta d\phi \,$
$\operatorname {div\ grad\ } f=\nabla \cdot (\nabla f)=\nabla ^{2}f=\Delta f$ (Laplace-Operator) $\operatorname {rot\ grad\ } f=\nabla \times (\nabla f)=0$ $\operatorname {div\ rot\ } \mathbf {A} =\nabla \cdot (\nabla \times \mathbf {A} )=0$ $\operatorname {rot\ rot\ } \mathbf {A} =\nabla \times (\nabla \times \mathbf {A} )=\nabla (\nabla \cdot \mathbf {A} )-\Delta \mathbf {A}$ $\Delta fg=f\Delta g+2\nabla f\cdot \nabla g+g\Delta f$ $\mathbf {A} \times (\mathbf {B} \times \mathbf {C} )=\mathbf {B} (\mathbf {A} \cdot \mathbf {C} )-(\mathbf {A} \cdot \mathbf {B} )\mathbf {C}$

Alphabet

Zeichen	Name	A.	gr.	N.	gr.
Α, α	Alpha (ἄλφα)	a	[a], [aː]	a	[a]
Β, β	Beta (βῆτα)	b	[b]	v	[v]
Γ, γ	Gamma (γάμμα)	g	[g]	g	[ɣ], [j]
Δ, δ	Delta (δέλτα)	d	[d]	d	[ð]
Ε, ε	Epsilon (ἔψιλον)	e	[e]	e	[ɛ]
Ζ, ζ	Zeta (ζῆτα)	z	[zd], [dz]	z	[z]
Η, η	Eta (ἦτα)	ē	[ɛː]	i	[i]
Θ, θ	Theta (θῆτα)	th	[tʰ]	th	[θ]
Ι, ι	Iota (ἰῶτα)	i	[i], [iː]	i	[i], [j]
Κ, κ	Kappa (κάππα)	k	[k]	k	[k], [kʲ]
Λ, λ	Lambda (λάμβδα)	l	[l]	l	[l]
Μ, μ	My (μῦ)	m	[m]	m	[m]
Ν, ν	Ny (νῦ)	n	[n]	n	[n]
Ξ, ξ	Xi (ξῖ)	x	[ks]	x	[ks]
Ο, ο	Omikron (ὄμικρον)	o	[o]	o	[ɔ]
Π, π	Pi (πῖ)	p	[p]	p	[p]
Ρ, ρ	Rho (ῥῶ)	r(h)	[r], [rʰ]	r	[r]
Σ, σ,ς	Sigma (σίγμα)	s	[s], [z]	s	[s], [z]
Τ, τ	Tau (ταῦ)	t	[t]	t	[t]
Υ, υ	Ypsilon (ὔψιλον)	y	[y], [yː]	y	[i]
Φ, φ	Phi (φῖ)	ph	[pʰ]	f	[f]
Χ, χ	Chi (χῖ)	ch	[kʰ]	ch	[x], [ç]
Ψ, ψ	Psi (ψῖ)	ps	[ps]	ps	[ps]
Ω, ω	Omega (ὠμέγα)	ō	[ɔː]	o	[ɔ]