Is the Quantum Casino's Use of Euler's Formula Misleading?

[mraptor]

On this page :
http://www.ipod.org.uk/reality/reality_quantum_casino.asp

the guy present a function like this :

ψ = A cos(x)

then he says according to Euler formula, which is e^ix = cos(x) + i sin(x) :

ψ = A e^ix ??

shouldn't the result be instead :

ψ + A*i*sin(x) = A cos(x) + A*i* sin(x)
ψ + A*i*sin(x) = A (cos(x) + i sin(x))
ψ = A e^ix - A*i*sin(x)
ψ = A (e^ix - i sin(x))

!

 

[mathman]

ψ=Re(Ae^ix), where Re means real part.

Your derivation of ψ has an error - last line should have -isin(x).

 

[torquil]

ψ=Re(Ae^ix), where Re means real part.

ψ=A Re(e^ix) is a bit better since it doesn't assume that A was real.

 

[mraptor]

ψ=Re(Ae^ix), where Re means real part.

If you take only the real part, why "i" stays in the equation afterward ?
How can a "Real" equation contains 'i' ?

What I meant to say.. is that if you take Re-part it has to stay inside Re-parenthesis the whole calculation isn't it ?

 

[Ken G]

How can a "Real" equation contains 'i' ?

You can take a real part of any complex number, so it's fine to have "i" inside the "Re".

What I meant to say.. is that if you take Re-part it has to stay inside Re-parenthesis the whole calculation isn't it ?

I believe what is happening is that some people assume so automatically that we will be taking the real part at the end that they simply don't bother to write "Re[]" in every expression-- but it's there anyway.

 

[jtbell]

On this page :
http://www.ipod.org.uk/reality/reality_quantum_casino.asp

the guy present a function like this :

ψ = A cos(x)

then he says according to Euler formula, which is e^ix = cos(x) + i sin(x) :

ψ = A e^ix ??

This is just plain sloppy. It's what you get for using a random Web site instead of a real textbook.