What Is the Conjugate of the Wave Function ψ(x)=R(x)e^(ikx)?

Thread starter chunhui219
Start date Apr 1, 2012
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Conjugate Function Wave Wave function

In summary, the conjugate of a wave function is the complex conjugate of the wave function, which represents the probability amplitude of a particle being at a particular position in space. It is calculated by taking the complex conjugate of the wave function, and has physical significance in the calculation of the probability density and expectation value of physical observables. It is a complex number and is related to the wave function through the Schrödinger equation.

Apr 1, 2012

chunhui219

if the wave function ψ(x)=R(x)e^ikx

then what is it conjugate, ψ*?

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Apr 1, 2012

tom.stoer

Science Advisor

chunhui219 said:

if the wave function ψ(x)=R(x)e^ikx

then what is it conjugate, ψ*?

I guess R is real; then you get ψ* = (R e^ikx)* = R* e^-ikx = R e^-ikx

Related to What Is the Conjugate of the Wave Function ψ(x)=R(x)e^(ikx)?

1. What is the conjugate of a wave function?

The conjugate of a wave function is the complex conjugate of the wave function, which represents the probability amplitude of a particle being at a particular position in space. It is denoted by the asterisk symbol ( * ) and is used to calculate the probability density of a particle.

2. How is the conjugate of a wave function calculated?

The conjugate of a wave function is calculated by taking the complex conjugate of the wave function, which involves changing the sign of the imaginary part of the function. For example, if the wave function is f(x) = 3 + 4i, the conjugate wave function would be f*(x) = 3 - 4i.

3. What is the physical significance of the conjugate of a wave function?

The conjugate of a wave function has physical significance as it gives the probability density of a particle at a specific position in space. It is used in the calculation of the expectation value of physical observables, such as position, momentum, and energy.

4. Can the conjugate of a wave function be a real number?

No, the conjugate of a wave function is a complex number. It is the complex conjugate of the wave function, which means it involves both a real and imaginary part. The real part represents the probability density, and the imaginary part represents the phase of the wave function.

5. What is the relationship between a wave function and its conjugate?

The wave function and its conjugate are related by the Schrödinger equation, which describes the time evolution of a quantum system. The product of the wave function and its conjugate gives the probability density of a particle at a particular position in space. They are also used to calculate the expectation value of physical observables.