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SandBoxMIWHall
  
last edited 9 years ago by Bill Page

Edit detail for SandBoxMIWHall revision 1 of 14
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Editor: Bill Page
Time: 2015/07/17 17:54:30 GMT+0
Note: 
changed:
-
Hall equations 15,19,20
\begin{axiom}
P:=operator('P)
g:=operator('g)
U:=operator('U)
r:=operator('r)
ℏ:=h
eq20:= g(q) = ℏ/2 * 1/P(q)*D(P(q),q)
eq19:= U(q) = 1/(2*m)*g(q)^2
eq15:= r(q) = -D(U(q),q)
eval(eq19,eq20)
eval(eq15,D(lhs %,q)=D(rhs %,q))
\end{axiom}

Hall equations 15,19,20

fricas
P:=operator('P)
\label{eq1}P(1)
Type: BasicOperator?
fricas
g:=operator('g)
\label{eq2}g(2)
Type: BasicOperator?
fricas
U:=operator('U)
\label{eq3}U(3)
Type: BasicOperator?
fricas
r:=operator('r)
\label{eq4}r(4)
Type: BasicOperator?
fricas
ℏ:=h
\label{eq5}h(5)
Type: Variable(h)
fricas
eq20:= g(q) = ℏ/2 * 1/P(q)*D(P(q),q)
\label{eq6}{g \left({q}\right)}={{h \ {{P_{\ }^{,}}\left({q}\right)}}\over{2 \ {P \left({q}\right)}}}(6)
Type: Equation(Expression(Integer))
fricas
eq19:= U(q) = 1/(2*m)*g(q)^2
\label{eq7}{U \left({q}\right)}={{{g \left({q}\right)}^{2}}\over{2 \ m}}(7)
Type: Equation(Expression(Integer))
fricas
eq15:= r(q) = -D(U(q),q)
\label{eq8}{r \left({q}\right)}= -{{U_{\ }^{,}}\left({q}\right)}(8)
Type: Equation(Expression(Integer))
fricas
eval(eq19,eq20)
\label{eq9}{U \left({q}\right)}={{{{h}^{2}}\ {{{P_{\ }^{,}}\left({q}\right)}^{2}}}\over{8 \ m \ {{P \left({q}\right)}^{2}}}}(9)
Type: Equation(Expression(Integer))
fricas
eval(eq15,D(lhs %,q)=D(rhs %,q))
\label{eq10}{r \left({q}\right)}={{-{{{h}^{2}}\ {P \left({q}\right)}\ {{P_{\ }^{,}}\left({q}\right)}\ {{P_{\ }^{, ,}}\left({q}\right)}}+{{{h}^{2}}\ {{{P_{\ }^{,}}\left({q}\right)}^{3}}}}\over{4 \ m \ {{P \left({q}\right)}^{3}}}}(10)
Type: Equation(Expression(Integer))