Definition of Momentum in terms of a partial derivative

In summary, Rahe is seeking clarification on a definition of momentum in a Quantum Mechanics video lecture. The definition involves ignoring certain terms and Rahe is unsure how this is done. The video lecture can be found at the 15:47 mark and it is suggested that the speaker may have just forgotten to include the terms in the video. The terms in question are derivatives with respect to other spherical coordinates that are not relevant in this case.
  • #1
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
 

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  • #2
Rahe said:
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?
 
  • #3
Chandra Prayaga said:
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.
 
  • #4
Rahe said:
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.

Rahe said:
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##).
 

1. What is momentum in terms of a partial derivative?

Momentum in terms of a partial derivative is a measure of an object's motion and its resistance to change in that motion. It is represented by the partial derivative of an object's position with respect to time.

2. How is momentum calculated using a partial derivative?

Momentum is calculated using the partial derivative of an object's position with respect to time. This is represented by the equation p = mv, where p is momentum, m is mass, and v is velocity.

3. What is the difference between momentum and velocity?

Momentum and velocity are related but different concepts. Velocity is a measure of an object's speed and direction, while momentum is a measure of an object's motion and resistance to change in that motion. In other words, velocity tells us how fast an object is moving, while momentum tells us how difficult it is to stop that object.

4. How is momentum conserved in a closed system?

In a closed system, the total momentum of all objects remains constant. This means that if two objects collide, their total momentum before the collision will be equal to their total momentum after the collision. This is known as the law of conservation of momentum.

5. What are some real-life examples of momentum in terms of a partial derivative?

Some real-life examples of momentum in terms of a partial derivative include a car moving at a constant speed, a ball rolling down a hill, and a rocket launching into space. In each of these cases, the object's momentum is determined by its mass and velocity.

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