Ket bra notation, and radial momentum

In summary, the conversation is about the equation <f|pr,g>=<prf|g> where pr is the operator for radial momentum and f and g are wavefunctions. The issue at hand is how to treat the comma in <f|pr,g>, with some suggesting it may be a typo in the book. The use of commas in kets is also discussed, with the conclusion that they are typically used to denote different quantum numbers. However, the notation pr,g may refer to two different quantum numbers for momentum. There is also a question about the notation pr being a quantum number or a symbol for the operator.
  • #1
Ed Quanta
297
0
I am told that <f|pr,g>=<prf|g> where pr is the operator for radial momentum and f and g are wavefunctions.

I know how to calculate <prf|g>, but I am not sure how to treat the comma in <f|pr,g>.

Anyone have an answer to this?
 
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  • #2
Ed Quanta said:
I am told that <f|pr,g>=<prf|g> where pr is the operator for radial momentum and f and g are wavefunctions.

I know how to calculate <prf|g>, but I am not sure how to treat the comma in <f|pr,g>.

Anyone have an answer to this?
Who was it that told you that? I've never see a comma used like that. It has no meaning to me. A wave function is in a one-to-one correspondance with a bra or a ket so I don't see what two wave functions mean in there.

Pete
 
  • #3
Maybe it is a typo in the book but I am not sure. I have only
seen commas used in kets when distinguishing between m and l values for angular momentum of a particle.
 
  • #4
the letters inside a bra or ket denote the quantum numbers of that state with respect to some operator.
the notation pr,g must just refer to 2 different quantum numbers
 
  • #5
Newton said:
the letters inside a bra or ket denote the quantum numbers of that state with respect to some operator.
the notation pr,g must just refer to 2 different quantum numbers

It's not possible...That "pr" is supposed to be [itex] \hat{p}_{r} [/itex] and not a quantum number.And besides,what quantum numbers are there for momentum??

Daniel.
 

1. What is Ket bra notation and how is it used in physics?

Ket bra notation is a mathematical notation used in quantum mechanics to represent the states of a quantum system. It consists of a ket symbol " | " and a bra symbol " < ", with the ket representing the state of a quantum system and the bra representing its dual state. This notation is used to describe the properties and behavior of particles at the quantum level.

2. How is radial momentum defined in quantum mechanics?

Radial momentum is a quantum mechanical quantity that describes the momentum of a particle in a radial direction. It is defined as the product of the magnitude of the momentum and the radial position of the particle. In other words, it measures how fast a particle is moving towards or away from a central point.

3. How is Ket bra notation used to calculate radial momentum?

In Ket bra notation, the radial momentum operator is represented by "p_r". To calculate the radial momentum of a quantum system, you would apply this operator to the ket representing the state of the system, and then take the inner product with the bra representing the dual state. This will give you the expectation value of the radial momentum for that particular state.

4. How does radial momentum relate to angular momentum in quantum mechanics?

In quantum mechanics, angular momentum and radial momentum are two types of momentum that together make up the total momentum of a particle. While angular momentum is related to the particle's rotational motion, radial momentum is related to its motion towards or away from a central point. Both of these momenta are important in understanding the behavior of particles at the quantum level.

5. What is the significance of radial momentum in quantum mechanics?

Radial momentum plays a crucial role in understanding the behavior of particles at the quantum level. It helps us to understand how particles move towards or away from a central point, and how their momentum affects their interactions with other particles. It is also closely related to the concept of energy, as changes in radial momentum can lead to changes in a particle's energy level.

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