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SandBoxMIWHall

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))