Expectation value of 1s state of hydrogen driving me absolutely nuts

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SUMMARY

The expectation value <1/r> of the 1s state of hydrogen is a critical concept in quantum mechanics. The correct interpretation of <1/r> leads to a result of 3/2 times the Bohr radius, contrasting with the incorrect calculation that yields 12 times the Bohr radius. The confusion arises from misinterpreting the notation, where <1/r> should not be confused with 1/. Understanding this distinction is essential for accurate calculations in quantum mechanics.

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  • Quantum mechanics fundamentals
  • Hydrogen atom wave functions
  • Bohr model of the atom
  • Expectation values in quantum mechanics
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doubleB
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My question says:

"Evaluate the expectation value <1/r> of the 1s state of hydrogen. How does this result compare to the result found using the Bohr theory?"

Firstly, I have been told that <1/r> does not mean <1/r> but rather that it means 1/<r>. Having made it this far I now do the 1/<r> and get about 12 times the bohr radius which is obviously wrong. Apparently the answer is 3/2 the bohr radius.
But also, I thought that doing <r> was supposed to give you 3/2 bohr radius, so what is this 1/<r> for?
Basically, what the hell is going on, in simple, clear terms?
Thank you for any help,
Ben
 
Physics news on Phys.org
1/<r> is wrong. It should be <1/r>.
 

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