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Edit detail for SandBoxMIWHall revision 2 of 14

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Editor: Bill Page
Time: 2015/07/17 18:04:06 GMT+0
Note:

changed:
-eval(eq15,D(lhs %,q)=D(rhs %,q))
RHall:=eval(eq15,D(lhs %,q)=D(rhs %,q))

added:

Gausssian
\begin{axiom}
PdfNorm(x)==1/2*sqrt(2)*exp(-1/2*x^2)/sqrt(%pi)
eval(RHall,[P(q)=PdfNorm(q),D(P(q),q)=D(PdfNorm(q),q),D(P(q),[q,q])=D(PdfNorm(q),[q,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
RHall:=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))

Gausssian

fricas
PdfNorm(x)==1/2*sqrt(2)*exp(-1/2*x^2)/sqrt(%pi)
Type: Void
fricas
eval(RHall,[P(q)=PdfNorm(q),D(P(q),q)=D(PdfNorm(q),q),D(P(q),[q,q])=D(PdfNorm(q),[q,q])])
fricas
Compiling function PdfNorm with type Variable(q) -> Expression(
      Integer)

\label{eq11}{r \left({q}\right)}= -{{{{h}^{2}}\  q}\over{4 \  m}}(11)
Type: Equation(Expression(Integer))