The conjugate of a Wave-Function

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In summary, the amplitude (A) of the wavefunction for a particle in a box can be represented by A = sqrt(2/L), where L is the length of the box. To show this, the wave equation \psi(x) = Asin((n*pi*x) / L) is used. To find the probability density function, the conjugate of the wave function must be found, which in this case is the function itself since it is a real-valued function.
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RCulling
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I'm trying to show that the amplitude (A) of the wavefunction for a particle in a box is:

A = sqrt(2/L) : L is the length of the box.

I'm using [tex]\psi[/tex](x) = Asin ((n*pi*x) / L) as the wave equation.

To do this I'm trying to integrate the probabilty density function from 0 through to L with respect to x.
But to find the probability density function I need to find the conjugate of the wave function. Which I don't know how to do.
Since there is no i (its a real valued function) does that mean it is its' own conjugate?

I really have no idea and can't seem to find anything on the net.

Thanks :)
 
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  • #2
The Hermitian conjugate of a real-valued function (square-integrable) is generally the function itself.
 
  • #3
Ok thanks a lot :)
 

FAQ: The conjugate of a Wave-Function

What is the conjugate of a wave-function?

The conjugate of a wave-function is a mathematical operation that involves taking the complex conjugate of each term in the wave-function. This results in a new wave-function with the same form as the original, but with the complex conjugate of each term.

Why is the conjugate of a wave-function important?

The conjugate of a wave-function is important because it helps us calculate physical quantities, such as probability, in quantum mechanics. It also allows us to work with real numbers instead of complex numbers, making calculations easier.

How is the conjugate of a wave-function related to the Schrödinger equation?

The Schrödinger equation is a fundamental equation in quantum mechanics that describes the time evolution of a wave-function. The conjugate of a wave-function is used to calculate the probability density, which is a key component of the Schrödinger equation.

Can the conjugate of a wave-function be negative?

Yes, the conjugate of a wave-function can be negative. The complex conjugate of a complex number is its mirror image in the complex plane, which means it can have a negative real or imaginary component.

How is the conjugate of a wave-function used in quantum mechanics experiments?

The conjugate of a wave-function is used in quantum mechanics experiments to calculate the probability of a particle being in a certain state or location. This information is crucial in understanding the behavior of particles at the quantum level.

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