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I’ve read that Ψ gives the amplitude and its square gives the probability of finding an electron according to the Schrodinger Wave Equation. Now, dimensionally amplitude is [L] and its square should be [L^2]. But probability is dimensionless. How is it possible? What are the correct dimensions of wave function?

I’ve read that  Ψ  gives the amplitude and its square gives the probability of finding an electron according to the Schrodinger Wave Equation. Now, dimensionally amplitude is [L] and its square should be [L^2]. But probability is dimensionless. How is it possible? What are the correct dimensions of wave function? 

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