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Question: How to simplify factors that are square roots into one single variable?

Question:How to simplify factors that are square roots into one single variable?

zenterix 405 Maple 2022
radical simplification
March 03 2025
0

In a calculation, I obtained the following expression from Maple.

> 

expr1:=A*sqrt(-m*(-V__0 + E))/sqrt(m*E)

A*(-m*(-V__0+E))^(1/2)/(m*E)^(1/2)

 (1)

The first question I have is why the "m's don't cancel."

Next, consider the expression

> 

expr2:=exp(sqrt(2)*sqrt(m)*sqrt(-V__0 + E)*l*I/`ℏ`)

exp(I*2^(1/2)*m^(1/2)*(-V__0+E)^(1/2)*l/`ℏ`)

 (2)
> 

simplify(expr2,[E-V__0=y])

exp(I*2^(1/2)*m^(1/2)*y^(1/2)*l/`ℏ`)

 (3)
> 

simplify(expr2,[2*m=y])

exp(I*y^(1/2)*(-V__0+E)^(1/2)*l/`ℏ`)

 (4)

Why doesn't the simplification below work?

> 

simplify(expr2,[2*m*(E-V__0)=y])

exp(I*2^(1/2)*m^(1/2)*(-V__0+E)^(1/2)*l/`ℏ`)

 (5)

I also tried with other commands

> 

eval(expr2,2*m=y)

exp(I*2^(1/2)*m^(1/2)*(-V__0+E)^(1/2)*l/`ℏ`)

 (6)
> 

eval(expr2,E-V__0=y)

exp(I*2^(1/2)*m^(1/2)*y^(1/2)*l/`ℏ`)

 (7)
> 

eval(expr2,2*m*(E-V__0)=y)

exp(I*2^(1/2)*m^(1/2)*(-V__0+E)^(1/2)*l/`ℏ`)

 (8)
> 

algsubs(2*m=y,expr2)

exp(I*y^(1/2)*(-V__0+E)^(1/2)*l/`ℏ`)

 (9)
> 

algsubs(E-V__0=y,expr2)

exp(I*2^(1/2)*m^(1/2)*y^(1/2)*l/`ℏ`)

 (10)
> 

algsubs(2*m*(E-V__0)=y,expr2)

exp(I*2^(1/2)*m^(1/2)*(-V__0+E)^(1/2)*l/`ℏ`)

 (11)
 

NULL

In reality, I would like to the entirety of sqrt(2m(E-V__0)/hbar) a variable by the name of s.

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