- #1
noblegas
- 268
- 0
Homework Statement
Find the conjugate of
[tex] \varphi[/tex]=[tex]exp(-x^2/x_0^2)[/tex]
Homework Equations
The Attempt at a Solution
Isn't the conjugate [tex] \varphi[/tex]*=[tex]exp(x^2/x_0^2)[/tex]
noblegas said:Homework Statement
Find the conjugate of
[tex] \varphi[/tex]=[tex]exp(-x^2/x_0^2)[/tex]
Homework Equations
The Attempt at a Solution
Isn't the conjugate [tex] \varphi[/tex]*=[tex]exp(x^2/x_0^2)[/tex]
Dick said:Not if x and x0 are real, which I suspect they are. What is it in that case?
noblegas said:oh ,my solution would only be correct if x/x0 is imaginary.would my expression
[tex]
exp(-x^2/x_0^2)
[/tex] not change when taking its conjugate??
Dick said:Right, sort of. If x is imaginary the conjugate(exp(x))=exp(-x). If x is real then conjugate(exp(x))=exp(x). But your solution is only correct if (x/x0)^2 is purely imaginary.
noblegas said:but x/x0 is not purely imaginary , but completely real. So my expression would remain the same when taking its conjugate
A conjugate of psi refers to the mathematical operation of finding the complex conjugate of the wave function psi. This is done by changing the sign of the imaginary component of psi.
The conjugate of psi is important in quantum mechanics as it is used in calculating the probability of finding a particle in a specific location. It is also used in finding the expectation value of a particle's position or momentum.
To find the conjugate of psi, you simply need to change the sign of the imaginary component of the wave function. If psi is written as psi(x) = A(x) + iB(x), then the conjugate of psi would be psi*(x) = A(x) - iB(x).
Yes, the conjugate of psi can be a complex number. This is because the wave function psi itself is a complex number, so its conjugate will also be a complex number.
No, the conjugate of psi is not always necessary in quantum mechanics. It is only needed in certain calculations, such as finding the probability of a particle's position or momentum. In other cases, it may not be relevant or needed.