Probability of a wave function

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SUMMARY

The discussion focuses on calculating the probability of finding an electron in the ground state of a hydrogen atom using its wave function. The method involves projecting the given wave function onto the ground state wave function of hydrogen. This process is rooted in the formalism of quantum mechanics, where wave functions are treated as vectors in Hilbert space. The probability is mathematically expressed as ||^2, where |a> represents the given state and |b> the ground state.

PREREQUISITES
  • Quantum mechanics fundamentals
  • Understanding of wave functions and Hilbert space
  • Linear algebra concepts, particularly vector projections
  • Knowledge of the hydrogen atom's ground state wave function
NEXT STEPS
  • Study the mathematical formulation of quantum mechanics
  • Learn about Hilbert space and its applications in quantum mechanics
  • Explore the properties of wave functions in quantum systems
  • Investigate the calculation of probabilities in quantum mechanics using projection methods
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Students and professionals in physics, particularly those specializing in quantum mechanics, as well as researchers interested in atomic structure and wave function analysis.

soul
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Hi everyone,

Assume that we have an electron in the Coulomb field of a proton, whose wave function is specified. How can I find the probability of finding this electron in the ground state of the hydrogen atom?

Thank you.
 
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find the projection of that given wave function with the wave function of ground state for hydrogen.
 
malawi_glenn said:
find the projection of that given wave function with the wave function of ground state for hydrogen.

Why do we do that? I couldn't understand the reason.
 
It is the formalism of quantum mechanics?

Think of vectors in the plane, wavefuctions are vectors in Hilbert space.

The probability for state |a> to be in state |b> is given by: |<a|b>|^2
 

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