Definition of Momentum in terms of a partial derivative

[Rahe]

Dear Members,

I was going through some video lecture (Quantum Mechanics) when I encountered a definition of momentum as shown in the attached picture.

I do not understand how iota and ħ is ignored ? There are some negligible terms after plus sign. What are those ? In short how they have defied this definition of Momentum ?

thanks
Rahe

 

[Chandra Prayaga]

Dear Members,

I was going through some video lecture (Quantum Mechanics) when I encountered a definition of momentum as shown in the attached picture.

I do not understand how iota and ħ is ignored ? There are some negligible terms after plus sign. What are those ? In short how they have defied this definition of Momentum ?

thanks
Rahe

Could you give a reference to the video lecture, and show more of that particular slide?

 

[Rahe]

Could you give a reference to the video lecture, and show more of that particular slide?

Thanks for the reply. Kindly find below the link.


The time is 15:47 where this definition is mentioned.

Thank you for the consideration.

 

[DrClaude]

The time is 15:47 where this definition is mentioned.

If you listen carefully, you will hear that she says "apart from $-i \hbar$, which we should remember to put in." The sound is a bit different, which hints at the fact that she just forgot to add the terms when the video was filmed, and the audio comment was added afterwards.

There are some negligible terms after plus sign. What are those ?

They are not negligible terms, they are the derivatives with respect to the other spherical coordinates ($\theta, \phi$), which are not relevant here (since they commute with $r$).