ਫਰਮਾ:ਕੁਆਂਟਮ ਮਕੈਨਿਕਸ ਓਪਰੇਟਰ

ਓਪਰੇਟਰ (ਸਾਂਝਾ ਨਾਮ)	ਕਾਰਟੀਜ਼ੀਅਨ ਕੰਪੋਨੈਂਟ	ਆਮ ਪਰਿਭਾਸ਼ਾ	SI ਯੂਨਿਟ	ਡਾਇਮੈਂਸ਼ਨ
ਪੁਜੀਸ਼ਨ	$\begin{array}{c}\hat{x}=x\\ \hat{y}=y\\ \hat{z}=z\end{array}$	$\widehat{𝐫}=𝐫$	m	[L]
ਮੋਮੈਂਟਮ	ਆਮ $\begin{array}{cc}{\hat{p}}_x& =-i\hslash \frac{\partial }{\partial x}\\ {\hat{p}}_y& =-i\hslash \frac{\partial }{\partial y}\\ {\hat{p}}_z& =-i\hslash \frac{\partial }{\partial z}\end{array}$	ਆਮ $\widehat{𝐩}=-i\hslash \mathrm{\nabla }$	J s m−1 = N s	[M] [L] [T]−1
	ਇਲੈਕਟ੍ਰੋਮੈਗਨੈਟਿਕ ਫੀਲਡ $\begin{array}{c}{\hat{p}}_x=-i\hslash \frac{\partial }{\partial x}-q{A}_x\\ {\hat{p}}_y=-i\hslash \frac{\partial }{\partial y}-q{A}_y\\ {\hat{p}}_z=-i\hslash \frac{\partial }{\partial z}-q{A}_z\end{array}$	ਇਲੈਕਟ੍ਰੋਮੈਗਨੈਟਿਕ ਫੀਲਡ (ਕਾਇਨੈਟਿਕ ਮੋਮੈਂਟਮ ਵਰਤਦਾ ਹੈ, A = ਵੈਕਟਰ ਪੁਟੇਂਸ਼ਲ) $\begin{array}{cc}\widehat{𝐩}& =\widehat{𝐏}-q𝐀\\ & =-i\hslash \mathrm{\nabla }-q𝐀\\ \end{array}$	J s m−1 = N s	[M] [L] [T]−1
ਕਾਇਨੈਟਿਕ ਐਨਰਜੀ	ਟ੍ਰਾਂਸਲੇਸ਼ਨ $\begin{array}{cc}{\hat{T}}_x& =-\frac{{\hslash }^2}{2m}\frac{{\partial }^2}{\partial x^2}\\ {\hat{T}}_y& =-\frac{{\hslash }^2}{2m}\frac{{\partial }^2}{\partial y^2}\\ {\hat{T}}_z& =-\frac{{\hslash }^2}{2m}\frac{{\partial }^2}{\partial z^2}\\ \end{array}$	$\begin{array}{cc}\hat{T}& =\frac{\widehat{𝐩}\cdot \widehat{𝐩}}{2m}\\ & =\frac{(-i\hslash \mathrm{\nabla })\cdot (-i\hslash \mathrm{\nabla })}{2m}\\ & =\frac{-{\hslash }^2}{2m}{\mathrm{\nabla }}^2\end{array}$	J	[M] [L]2 [T]−2
	ਇਲੈਕਟ੍ਰੋਮੈਗਨੈਟਿਕ ਫੀਲਡ $\begin{array}{cc}{\hat{T}}_x& =\frac{1}{2m}{(-i\hslash \frac{\partial }{\partial x}-q{A}_x)}^2\\ {\hat{T}}_y& =\frac{1}{2m}{(-i\hslash \frac{\partial }{\partial y}-q{A}_y)}^2\\ {\hat{T}}_z& =\frac{1}{2m}{(-i\hslash \frac{\partial }{\partial z}-q{A}_z)}^2\end{array}$	ਇਲੈਕਟ੍ਰੋਮੈਗਨੈਟਿਕ ਫੀਲਡ (A = ਵੈਕਟਰ ਪੁਟੈਂਸ਼ਲ) $\begin{array}{cc}\hat{T}& =\frac{\widehat{𝐩}\cdot \widehat{𝐩}}{2m}\\ & =\frac{1}{2m}(-i\hslash \mathrm{\nabla }-q𝐀)\cdot (-i\hslash \mathrm{\nabla }-q𝐀)\\ & =\frac{1}{2m}(-i\hslash \mathrm{\nabla }-q𝐀{)}^2\end{array}$	J	[M] [L]2 [T]−2
	ਰੋਟੇਸ਼ਨ (I = ਇਨ੍ਰਸ਼ੀਆ ਦੀ ਮੋਮੈਂਟ) $\begin{array}{cc}{\hat{T}}_{xx}& =\frac{{\hat{J}}_x^2}{2I_{xx}}\\ {\hat{T}}_{yy}& =\frac{{\hat{J}}_y^2}{2I_{yy}}\\ {\hat{T}}_{zz}& =\frac{{\hat{J}}_z^2}{2I_{zz}}\\ \end{array}$	ਰੋਟੇਸ਼ਨ $\hat{T}=\frac{\widehat{𝐉}\cdot \widehat{𝐉}}{2I}$ਫਰਮਾ:Citation needed	J	[M] [L]2 [T]−2
ਪੁਟੇਂਸ਼ਲ ਐਨਰਜੀ	N/A	$\hat{V}=V(𝐫,t)=V$	J	[M] [L]2 [T]−2
ਕੁੱਲ ਐਨਰਜੀ	N/A	ਸਮੇਂ-ਤੇ-ਨਿਰਭਰ ਪੁਟੈਂਸ਼ਲ: $\hat{E}=i\hslash \frac{\partial }{\partial t}$ ਸਮੇਂ-ਤੇ-ਨਿਰਭਰ: $\hat{E}=E$	J	[M] [L]2 [T]−2
ਹੈਮਿਲਟੋਨੀਅਨ		$\begin{array}{cc}\hat{H}& =\hat{T}+\hat{V}\\ & =\frac{\widehat{𝐩}\cdot \widehat{𝐩}}{2m}+V\\ & =\frac{{\hat{p}}^2}{2m}+V\\ \end{array}$	J	[M] [L]2 [T]−2
ਐਂਗੁਲਰ ਮੋਮੈਂਟਮ ਓਪਰੇਟਰ	$\begin{array}{cc}{\hat{L}}_x& =-i\hslash (y\frac{\partial }{\partial z}-z\frac{\partial }{\partial y})\\ {\hat{L}}_y& =-i\hslash (z\frac{\partial }{\partial x}-x\frac{\partial }{\partial z})\\ {\hat{L}}_z& =-i\hslash (x\frac{\partial }{\partial y}-y\frac{\partial }{\partial x})\end{array}$	$\widehat{𝐋}=𝐫\times -i\hslash \mathrm{\nabla }$	J s = N s m−1	[M] [L]2 [T]−1
ਸਪਿੱਨ ਐਂਗੁਲਰ ਮੋਮੈਂਟਮ	$\begin{array}{c}{\hat{S}}_x=\frac{\hslash }{2}{\sigma }_x\\ {\hat{S}}_y=\frac{\hslash }{2}{\sigma }_y\\ {\hat{S}}_z=\frac{\hslash }{2}{\sigma }_z\end{array}$ ਜਿੱਥੇ ${\sigma }_x=\left(\begin{array}{cc}0& 1\\ 1& 0\end{array}\right)$ ${\sigma }_y=\left(\begin{array}{cc}0& -i\\ i& 0\end{array}\right)$ ${\sigma }_z=\left(\begin{array}{cc}1& 0\\ 0& -1\end{array}\right)$ ਸਪਿੱਨ-½ ਕਣਾਂ ਵਾਸਤੇ ਪੌਲੀ ਮੈਟ੍ਰਿਕਸ ਹਨ।	$\widehat{𝐒}=\frac{\hslash }{2}\mathit{\sigma }$ ਜਿੱਥੇ σ ਪੌਲੀ ਮੈਟ੍ਰਿਕਸਾਂ ਨਾਮਕ ਕੰਪੋਨੈਂਟਾਂ ਦਾ ਵੈਕਟਰ ਹੁੰਦਾ ਹੈ।	J s = N s m−1	[M] [L]2 [T]−1
ਕੁੱਲ ਐਂਗੁਲਰ ਮੋਮੈਂਟਮ	$\begin{array}{cc}{\hat{J}}_x& ={\hat{L}}_x+{\hat{S}}_x\\ {\hat{J}}_y& ={\hat{L}}_y+{\hat{S}}_y\\ {\hat{J}}_z& ={\hat{L}}_z+{\hat{S}}_z\end{array}$	$\begin{array}{cc}\widehat{𝐉}& =\widehat{𝐋}+\widehat{𝐒}\\ & =-i\hslash 𝐫\times \mathrm{\nabla }+\frac{\hslash }{2}\mathit{\sigma }\end{array}$	J s = N s m−1	[M] [L]2 [T]−1
ਟ੍ਰਾਂਜ਼ੀਸ਼ਨ ਡਾਈਪੋਲ ਮੋਮੈਂਟ (ਇਲੈਕਟ੍ਰਿਕ)	$\begin{array}{cc}{\hat{d}}_x& =q\hat{x}\\ {\hat{d}}_y& =q\hat{y}\\ {\hat{d}}_z& =q\hat{z}\end{array}$	$\widehat{𝐝}=q\widehat{𝐫}$	C m	[I] [T] [L]