Continuity of the wave function

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The continuity of the wave function and its first derivative in quantum mechanics is debated, with some arguing it is essential for defining probabilities and ensuring physical significance, while others contend that discontinuities can still yield valid wave functions. The discussion highlights that wave functions need to be square integrable and often continuous to satisfy the Schrödinger equation, which is crucial for making accurate predictions. Some participants suggest that the continuity requirement may stem from the mathematical framework rather than physical necessity, as certain idealizations like infinite potential wells can lead to discontinuities. The conversation also touches on the role of distributions in quantum mechanics, indicating that while wave functions are typically continuous, there are scenarios where discontinuous functions can still be meaningful. Ultimately, the continuity of the wave function is seen as fundamental for ensuring well-defined probabilities in quantum mechanics.
  • #31
actually i have my exam and i am really weak in quantum mechanics ... i would like to know another question sir ... i know the physical meaning of normalization , will you please tell me the physical meaning of orthogonality ? i have one more small assignment too .. i tried but unable to do ... the question is that if H is an operator of an eigen function U1 with eigen value E1 and H is an operator of an eigen function U2 with eigen value E2 then show that H is also an operator of the eigen function U1+U2.
 
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  • #32
pi11 said:
actually i have my exam and i am really weak in quantum mechanics ... i would like to know another question sir ... i know the physical meaning of normalization , will you please tell me the physical meaning of orthogonality ? i have one more small assignment too .. i tried but unable to do ... the question is that if H is an operator of an eigen function U1 with eigen value E1 and H is an operator of an eigen function U2 with eigen value E2 then show that H is also an operator of the eigen function U1+U2.

This really belongs in the homework help section.

But I will answer the orthogonality question by asking you to apply the Born rule to orthogonal states.

Since they are eigenfunctions H*U1 = E1*U1 and H*U1 = E1*U1 so H*(U1 +U2) = H*(E1 + E2) so E1 + E2 is an eigenvalue of H with eigenfunction U1+U2.

Thanks
Bill
 

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