What are the units of a wave function

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The discussion centers on the units of a wave function in quantum mechanics, with the initial intuition suggesting it is unitless. However, since the magnitude squared of the wave function represents a probability density, it must have units of 1 over some power of length, specifically 1/L^(n/2) where n is the dimension. Participants confirm that there is no error in this reasoning. A referenced article is provided for further reading on the topic. The conversation reinforces the understanding of wave function units in relation to probability density.
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My intuition is that it would be unitless. But if it's magnitude squared is a probability density, then its units would have to be 1 over some power of length. Specifically 1/L^(n/2) where n is the dimension. Where's the error in my thought? Thanks
 
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No error. You're right.
 
Thanks guys. That's a nice article also.
 

Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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