constant, denoted ℏ {\textstyle \hbar } (h-bar), equal to the Planck constant divided by 2π: ℏ = h 2 π {\textstyle \hbar ={\frac {h}{2\pi }}} , is commonly...

Ħ (minuscule: ħ) is a letter of the Latin alphabet, derived from H with the addition of a bar. It is used in Maltese for a voiceless pharyngeal fricative...

prefix h, meaning 100 times. H with diacritics: Ĥ ĥ Ȟ ȟ Ħ ħ Ḩ ḩ Ⱨ ⱨ ẖ ẖ Ḥ ḥ Ḣ ḣ Ḧ ḧ Ḫ ḫ ꞕ Ꜧ ꜧ IPA-specific symbols related to H: ʜ ɦ ʰ ʱ ɥ ᶣ ɧ Superscript...

ɹ̠̊˔ ɹ̠˔ ɻ̊˔ ɻ˔ ç ʝ x ɣ χ ʁ ħ ʕ h ɦ Approximant ʋ ɹ ɻ j ɰ ʔ̞ Tap/flap ⱱ̟ ⱱ ɾ̼ ɾ̥ ɾ ɽ̊ ɽ ɢ̆ ʡ̆ Trill ʙ̥ ʙ r̥ r ɽ̊r̥ ɽr ʀ̥ ʀ ʜ ʢ Lateral affricate tɬ dɮ tꞎ...

in 1928: σ x σ p ≥ ℏ 2 {\displaystyle \sigma _{x}\sigma _{p}\geq {\frac {\hbar }{2}}} where ℏ = h 2 π {\displaystyle \hbar ={\frac {h}{2\pi }}} is the reduced...

the International Phonetic Alphabet that represents this sound is an h-bar, ⟨ħ⟩, and the equivalent X-SAMPA symbol is X\. In the transcription of Arabic...

amount to Hermite functions, ψ n ( x ) = 1 2 n n ! ( m ω π ℏ ) 1 / 4 e − m ω x 2 2 ℏ H n ( m ω ℏ x ) , n = 0 , 1 , 2 , … . {\displaystyle \psi _{n}(x)={\frac...

U ( t ) − i ℏ U † ( t ) A S ( t ) U ( t ) U † ( t ) H S ( t ) U ( t ) + ( ∂ A S ∂ t ) H = i ℏ [ H H ( t ) , A H ( t ) ] + ( ∂ A S ∂ t ) H , {\displaystyle...

i ℏ ∫ t 0 t d t 1 e i ℏ λ V ( t 1 − t 0 ) H 0 e − i ℏ λ V ( t 1 − t 0 ) − 1 ℏ 2 ∫ t 0 t d t 1 ∫ t 0 t 1 d t 2 e i ℏ λ V ( t 1 − t 0 ) H 0 e − i ℏ λ V...

) = e i H 0 , S t / ℏ H 1 , S e − i H 0 , S t / ℏ , {\displaystyle H_{1,{\text{I}}}(t)=\mathrm {e} ^{\mathrm {i} H_{0,{\text{S}}}t/\hbar }H_{1,{\text{S}}}\mathrm...

equation for a single nonrelativistic particle in one dimension: i ℏ ∂ ∂ t Ψ ( x , t ) = [ − ℏ 2 2 m ∂ 2 ∂ x 2 + V ( x , t ) ] Ψ ( x , t ) . {\displaystyle...

the values of the following discrete set: s z ∈ { − s ℏ , − ( s − 1 ) ℏ , … , + ( s − 1 ) ℏ , + s ℏ } . {\displaystyle s_{z}\in \{-s\hbar ,-(s-1)\hbar ...

eigenstates are given by ψ n ( x ) = 1 2 n n ! ⋅ ( m ω π ℏ ) 1 / 4 ⋅ e − m ω x 2 2 ℏ ⋅ H n ( m ω ℏ x ) , {\displaystyle \psi _{n}(x)={\sqrt {\frac {1}{2^{n}\...

2 = − ( i 2 m c 2 ℏ ∂ ϕ ∂ t + ( m c 2 ℏ ) 2 ϕ − ∂ 2 ϕ ∂ t 2 ) e − i ℏ m c 2 t ≈ − ( i 2 m c 2 ℏ ∂ ϕ ∂ t + ( m c 2 ℏ ) 2 ϕ ) e − i ℏ m c 2 t {\displaystyle...

commutation relations with each other: [ L x , L y ] = i ℏ L z , [ L y , L z ] = i ℏ L x , [ L z , L x ] = i ℏ L y , {\displaystyle \left[L_{x},L_{y}\right]=i\hbar...

pharyngeal /ħ/, or velar /x/. In Arabic, two corresponding letters were created for both phonemic sounds: unmodified ḥāʾ ح represents /ħ/, while ḫāʾ خ...

d Q ^ d t = i ℏ [ H ^ , Q ^ ] {\displaystyle {\frac {d{\hat {Q}}}{dt}}={\frac {i}{\hbar }}[{\hat {H}},{\hat {Q}}]} d P ^ d t = i ℏ [ H ^ , P ^ ] . {\displaystyle...

) = 1 ℏ ∑ k = 0 ∞ ℏ k A k ( x ) {\displaystyle A(x)={\frac {1}{\hbar }}\sum _{k=0}^{\infty }\hbar ^{k}A_{k}(x)} and B ( x ) = 1 ℏ ∑ k = 0 ∞ ℏ k B k (...

H ^ = − ℏ 2 2 ∑ i = 1 N 1 m i ∇ i 2 + ∑ i = 1 N V i = ∑ i = 1 N ( − ℏ 2 2 m i ∇ i 2 + V i ) = ∑ i = 1 N H ^ i {\displaystyle {\begin{aligned}{\hat {H}}&=-{\frac...

mass m in one dimension is defined as j = ℏ 2 m i ( Ψ ∗ ∂ Ψ ∂ x − Ψ ∂ Ψ ∗ ∂ x ) = ℏ m ℜ { Ψ ∗ 1 i ∂ Ψ ∂ x } = ℏ m ℑ { Ψ ∗ ∂ Ψ ∂ x } , {\displaystyle j={\frac...

i ℏ H Φ {\displaystyle {\frac {\partial \Phi }{\partial t}}={\frac {1}{i\hbar }}H\Phi } By taking the complex conjugate we find ∂ Φ ∗ ∂ t = − 1 i ℏ Φ...

= h ν = h c λ = h c ν ~ , {\displaystyle E=h\nu ={\frac {hc}{\lambda }}=hc{\tilde {\nu }},} as well as the following "angular" forms: E = ℏ ω = ℏ c y...

H-bar or h-bar can refer to: H with stroke, a Latin letter H with a doubled horizontal stroke (Ħ ħ) Voiceless pharyngeal fricative, represented in IPA...

term we can write ∑ n = 0 ∞ n e − n β ℏ ω = − ∂ ∂ ( β ℏ ω ) ( ∑ n = 0 ∞ e − n β ℏ ω ) = e − β ℏ ω ( 1 − e − β ℏ ω ) 2 . {\displaystyle \sum _{n=0}^{\infty...

unit system uses the following defining constants: c, ℏ, G, kB, where c is the speed of light, ℏ is the reduced Planck constant, G is the gravitational...

ℏ ω 0 − ℏ 2 k ⋅ q m ≃ 1 + V q ℏ ω 0 ∑ k , i q i ∂ f k ∂ k i ( 1 + ℏ k ⋅ q m ω 0 ) ≃ 1 + V q ℏ ω 0 ∑ k , i q i ∂ f k ∂ k i ℏ k ⋅ q m ω 0 = 1 + V q ℏ ω...

and Jz: | α | 2 = ℏ 2 j ( j + 1 ) − ℏ 2 m 2 − ℏ 2 m = ℏ 2 ( j − m ) ( j + m + 1 ) , | β | 2 = ℏ 2 j ( j + 1 ) − ℏ 2 m 2 + ℏ 2 m = ℏ 2 ( j + m ) ( j −...

Δ x Δ p ≥ ℏ 2 , {\displaystyle \Delta x\,\Delta p\geq {\frac {\hbar }{2}},} so the uncertainty in the particle's momentum satisfies Δ p ≥ ℏ 2 Δ x . {\displaystyle...

^ eff = − i ℏ ∇ + ℏ k , {\displaystyle {\hat {\mathbf {p} }}_{\text{eff}}=-i\hbar \nabla +\hbar \mathbf {k} ,} a standard momentum − i ℏ ∇ {\displaystyle...

to a normalizing constant, ⟨ Q | e − i H t ℏ | ψ ⟩ = ∑ j Q j e − E j i t ℏ ⟨ j | j ⟩ = ∑ j Q j e − E j i t ℏ . {\displaystyle \left\langle Q\left|e^{-{\frac...