Quantum Physics-Perturbations

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In summary, the conversation discusses finding an expression for the correction to the energy of the ground state of the hydrogen atom caused by the finite size of the nucleus. The approach suggested is to treat the nuclear charge as a thin shell of radius r0 and consider it as a perturbation. The conversation also mentions the need to factor in the shift in potential energy resulting from the difference between the point charge and the shell charge distribution. The person is seeking additional guidance in solving this problem.
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andyfreesty1e
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Homework Statement


Find an expression for the correction to the energy of the ground state of the hydrogen atom due to the finite size of the nucleus. Treat the nuclear charge as a thin shell of radius r0.

what i have been thinking is that you the size of the nucleus as a perturbation, but i don't know where to go from here.

Just really looking for a step in the right direction
Thanks
 
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There will be a shift in the potential energy resulting from the difference between the point charge (presumably this is what your model previously assumed) and the shell charge distribution.

Another hint:

The energy shift will be <psi*(r)|delta V |psi(r)>

And another:

The difference in potential is only really significant over a range of r much less than the Bohr radius, so the wavefunctions are essentially constant and can be taken outside the integral. Don't forget the 4pi r^2 in the integral over space.
 

1. What is quantum physics-perturbations?

Quantum physics-perturbations refer to small disturbances or changes in the behavior of quantum systems, which are systems that involve subatomic particles and operate according to the principles of quantum mechanics.

2. What causes perturbations in quantum systems?

Perturbations in quantum systems can be caused by a variety of factors, such as external forces or interactions with other particles. They can also arise due to the inherent probabilistic nature of quantum mechanics.

3. How do perturbations affect quantum systems?

Perturbations can have a significant impact on the behavior of quantum systems. They can cause changes in the state or properties of the particles involved, and can also lead to the phenomenon of quantum entanglement, where particles become correlated and affect each other's behavior.

4. Can perturbations be controlled or predicted in quantum systems?

While perturbations in quantum systems are inherently unpredictable, scientists have developed techniques to control and manipulate them to a certain extent. This allows for the study and utilization of quantum effects in various fields, such as quantum computing and quantum cryptography.

5. What are the practical applications of studying quantum physics-perturbations?

Studying quantum physics-perturbations has led to numerous advancements in technology, such as the development of more efficient and secure communication systems and the potential for faster and more powerful computers. It also allows for a deeper understanding of the fundamental nature of the universe and its smallest building blocks.

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