Solve for a normaliztion constant in MATLAB

Hi, I have the following code:

if true
  % code
end
syms h g x C n L p e E C m N
y = - (exp(-(x*(g*1i + (- 2*g^2 + E)^(1/2)))/h)*(g*1i - (- 2*g^2 + E)^(1/2)))/(2*(E - 2*g^2)^(1/2)) + (exp(-(x*(g*1i - (- 2*g^2 + E)^(1/2)))/h)*(g*1i + (- 2*g^2 + E)^(1/2)))/(2*(E - 2*g^2)^(1/2))
z = - (exp(-(x*(g*(-i) + (- 2*g^2 + E)^(1/2)))/h)*(g*(-i) - (- 2*g^2 + E)^(1/2)))/(2*(E - 2*g^2)^(1/2)) + (exp(-(x*(g*(-i) - (- 2*g^2 + E)^(1/2)))/h)*(g*(-i) + (- 2*g^2 + E)^(1/2)))/(2*(E - 2*g^2)^(1/2))
prod=@(x)y(x).*z(x)*N^2
Nsol = solve(int(prod,x,0,2*pi)-1==0,N)
A=vpa(Nsol)

all constants are defined (not visible to save space), and I would like to solve for N, as can be seen in prod line, but this does not work.

This gives however:

Error in sym>tomupad (line 1233) x = funchandle2ref(x);

Error in sym (line 199) S.s = tomupad(x);

Error in sym/int (line 63) f = sym(f);

Error in Integral_eqn (line 15) Nsol = solve(int(prod,x,0,2*pi)-1==0,N)

Answer 1

[Torsten]

Does it work if you simply set

prod = y*z*N^2;

?

By the way: The result will be

N = +/- 1/sqrt(int(y*z,x,0,2*pi))

Best wishes

Torsten.

[Sergio Manzetti]

Didn't work for me, but I take your result for good! Thanks Torsten,

[Torsten]

What's the error message for this coding:

syms h g x C n L p e E C m N
y = - (exp(-(x*(g*1i + (- 2*g^2 + E)^(1/2)))/h)*(g*1i - (- 2*g^2 + E)^(1/2)))/(2*(E - 2*g^2)^(1/2)) + (exp(-(x*(g*1i - (- 2*g^2 + E)^(1/2)))/h)*(g*1i + (- 2*g^2 + E)^(1/2)))/(2*(E - 2*g^2)^(1/2))
z = - (exp(-(x*(g*(-i) + (- 2*g^2 + E)^(1/2)))/h)*(g*(-i) - (- 2*g^2 + E)^(1/2)))/(2*(E - 2*g^2)^(1/2)) + (exp(-(x*(g*(-i) - (- 2*g^2 + E)^(1/2)))/h)*(g*(-i) + (- 2*g^2 + E)^(1/2)))/(2*(E - 2*g^2)^(1/2))
prod = N^2*y*z;
Nsol = solve(int(prod,x,0,2*pi)-1==0,N)

?

Best wishes

Torsten.

Answer 2

[Birdman]

Use the following:

syms h g y(x) z(x) C n L p e E C m N
y(x) = - (exp(-(x*(g*1i + (- 2*g^2 + E)^(1/2)))/h)*(g*1i - (- 2*g^2 + E)^(1/2)))/(2*(E - 2*g^2)^(1/2)) + (exp(-(x*(g*1i - (- 2*g^2 + E)^(1/2)))/h)*(g*1i + (- 2*g^2 + E)^(1/2)))/(2*(E - 2*g^2)^(1/2))
z(x) = - (exp(-(x*(g*(-i) + (- 2*g^2 + E)^(1/2)))/h)*(g*(-i) - (- 2*g^2 + E)^(1/2)))/(2*(E - 2*g^2)^(1/2)) + (exp(-(x*(g*(-i) - (- 2*g^2 + E)^(1/2)))/h)*(g*(-i) + (- 2*g^2 + E)^(1/2)))/(2*(E - 2*g^2)^(1/2))
prod=y.*z.*N.^2
Nsol = solve(int(prod,x,0,2*pi)-1==0,N)
A=vpa(Nsol)

[Sergio Manzetti]

Thanks Birdman, it gave the result. Quite a horrible one ! Thanks!

[Birdman]

If it did, can you accept the answer?