Quantum Physics Question - Second Year University level.

In summary, the conversation is about finding the normalisation constant for an antisymmetric eigenfunction of the helium atom. The conversation includes a question and a potential solution, with the conclusion that the eigenfunction must be divided by the square root of 2 to achieve a normalisation constant of 1.
  • #1
coffeem
91
0
Hi there,

I have some questions which I cannot solve from my Quantum book. I would appretiate some hints as to how they should be solved. Thanks.

Question

The antisymmetric eigenfunction of the helium atom can be written in the form UA - C(uab-uba), where uab and uba are orthonormal. Show that the normalisation constant C = 1/root(2).
 
Physics news on Phys.org
  • #2
Hi coffeem! :smile:
coffeem said:
The antisymmetric eigenfunction of the helium atom can be written in the form UA - C(uab-uba), where uab and uba are orthonormal. Show that the normalisation constant C = 1/root(2).

well, that means you have to prove that (uab-uba)(uab-uba)* = 2 :wink:
 
  • #3
tiny-tim said:
Hi coffeem! :smile:


well, that means you have to prove that (uab-uba)(uab-uba)* = 2 :wink:

Thanks for your help, I really do appreciate it. I can expand the brackets and get:

UabUab + UbaUba = 2 (since UabUba = 0)

So would a reasonable answer be:

Since (Uab-Uba)^2 is 2, to normalise this to 1, we must divide the eigenfunction by the square root of this?

Thanks.
 
  • #4
coffeem said:
Thanks for your help, I really do appreciate it. I can expand the brackets and get:

UabUab + UbaUba = 2 (since UabUba = 0)

So would a reasonable answer be:

Since (Uab-Uba)^2 is 2, to normalise this to 1, we must divide the eigenfunction by the square root of this?

Thanks.

Yes, except I'd say "we must divide it by the square root" …

any multiple of (Uab-Uba) is an eigenfunction. :wink:
 

1. What is quantum physics?

Quantum physics is a branch of physics that studies the behavior and interactions of particles at the subatomic level. It involves principles such as wave-particle duality, uncertainty principle, and superposition, which are different from the classical laws of physics.

2. What are the applications of quantum physics?

Quantum physics has many practical applications, including in technology, medicine, and encryption. Some examples include transistors, lasers, MRI machines, and quantum cryptography.

3. How does quantum physics relate to relativity?

Quantum physics and relativity are two major theories in physics that describe different aspects of the universe. While quantum physics deals with the behavior of particles at the subatomic level, relativity explains the behavior of objects at a larger scale. However, both theories are needed to fully understand the workings of the universe.

4. What is the difference between quantum mechanics and quantum field theory?

Quantum mechanics is a mathematical framework that describes the behavior of particles at the subatomic level. On the other hand, quantum field theory is a more advanced version of quantum mechanics that incorporates the principles of special relativity and allows for the study of fields and interactions between particles.

5. How does quantum physics challenge our understanding of reality?

Quantum physics introduces concepts that challenge our classical understanding of reality, such as superposition and wave-particle duality. It also suggests that the act of observation can affect the behavior of particles, leading to the famous thought experiment of Schrödinger's cat. These concepts have sparked debates and discussions about the nature of reality and our perception of it.

Similar threads

Replies
6
Views
767
  • STEM Career Guidance
Replies
11
Views
596
Replies
1
Views
725
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
824
Replies
4
Views
1K
Replies
26
Views
2K
Replies
1
Views
263
  • Introductory Physics Homework Help
Replies
1
Views
1K
Back
Top