Hydrogen atom ground state wave function complex conjugate

In summary, we discussed the hydrogen atom ground state wavefunction, which is given by φ=π-1/2a-3/2e-r/1. We also talked about the complex conjugate of φ*, which is itself since φ is real. The complex conjugate of a complex number is its conjugate. We also mentioned the kinetic energy operator, T, and its role in the calculation of ∫φ*Tφdτ.
  • #1
zqz51911
6
0
For hydrogen atom ground state
we know φ=π-1/2a-3/2e-r/1
I want to know the complex conjugate of φ* ?
 
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  • #2
What do you know about complex numbers?
Note: just a reminder that the complex conjugate of ##z^*## is ##(z^*)^*##.
 
  • #3
I need do a calculation for ∫φ*Tφdτ T is the kinetic energy operator , I did not how to type the ∧ over T
 
  • #4
zqz51911 said:
∫φ*Tφdτ
Is the integration variable T? What is T?
What do you think about the nature of the ground state wavefunction of H atom, is it real or complex?
 
  • #5
T is the kinetic energy operator
integration is not variable T
I just want to know the complex conjugate of φ
I think i figure it out , due to the φ is real, the complex conjugate of φ is itself . thanks anyway
 

1. What is the "ground state" of a hydrogen atom?

The ground state of a hydrogen atom refers to the lowest possible energy level that an electron can occupy. This is the most stable state for the atom.

2. What is a "wave function" in the context of a hydrogen atom?

A wave function is a mathematical representation of the probability of finding an electron at a certain position around the nucleus of a hydrogen atom. It describes the behavior of the electron in space.

3. What does "complex conjugate" mean in relation to the hydrogen atom ground state wave function?

The complex conjugate is a mathematical operation that flips the sign of the imaginary part of a complex number. In the context of the hydrogen atom ground state wave function, the complex conjugate is used to ensure that the total probability of finding an electron in all possible positions around the nucleus is equal to 1.

4. Why is the complex conjugate necessary in the hydrogen atom ground state wave function?

The complex conjugate is necessary because the wave function of a hydrogen atom is a complex-valued function. Without taking the complex conjugate, the probability of finding an electron in a certain position would be negative, which is not physically meaningful.

5. How does the complex conjugate affect the shape of the hydrogen atom ground state wave function?

The complex conjugate does not affect the shape of the hydrogen atom ground state wave function. It only ensures that the total probability of finding an electron in all possible positions is equal to 1, which is necessary for the wave function to accurately describe the behavior of the electron in space.

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