The difference between spatial and intrinsic parity

In summary, the difference between intrinsic and extrinsic parity in Griffiths QM is that intrinsic parity is specific to each particle and describes how its state changes under a parity transformation, while extrinsic parity is determined by the orbital angular momentum and can be influenced by the configuration of multiple particles. Intrinsic parity is the eigenvalue of the operator that switches all the signs in the position wavefunction, while extrinsic parity is given by (-1)^l, where l is the orbital angular momentum. This means that a single fundamental particle will have only intrinsic parity, while a composite or group of particles may have both intrinsic and extrinsic parity. The sign of the parity is simply a matter of convention.
  • #1
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Can someone explain on the level of Griffiths QM what the difference between those two parities since I'm quite confused here. Some sources use the terms interchangably, some don't.

Could anyone provide good definitions for both terms?

Spatial parity seems pretty obvious to me to be the eigenvalue associated with an eigenstate of the position vector inversion.
 
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  • #2
In general the parity of a particle is the product of intrinsic and extrinsic (or spatial as you say) parity. Extrinsic parity is given by ##(-1)^l## where ##l## is the orbital angular momentum of the state. Intrinsic parity is peculiar of each particle and it simply says as the state of the particle change under a parity transformation:
$$
P\vert \pi\rangle=\vert \pi\rangle\quad\text{for positive parity}
$$
$$
P\vert \pi\rangle=-\vert \pi\rangle\quad\text{for negative parity}
$$
 
  • #3
Firs off, thanks for the answer.

Right,so the intrinsic parity is the eigenvalue of the operator that switches all the signs in the position wavefunction?

How does extrinsic parity relate to this operator and eigenvalue?
 
  • #4
a single fundamental particle (like a single quark) will have intrinsic parity.
a composite or a group of particle(s) will have intrinsic parity (due to the constituents/members) + maybe extrinsic parity (due to the configuration of those particles).
The sign is just a matter of convention.
 

FAQ: The difference between spatial and intrinsic parity

What is spatial parity?

Spatial parity, also known as left-right parity or mirror symmetry, refers to the concept of symmetry in physical space. It is the property of an object or system being unchanged when reflected or rotated in space.

What is intrinsic parity?

Intrinsic parity, also known as chirality or handedness, refers to the property of an object or system being unchanged when reflected in an internal symmetry. This type of parity is often seen in molecules and subatomic particles.

What is the difference between spatial and intrinsic parity?

The main difference between spatial and intrinsic parity is the type of symmetry that is being considered. Spatial parity refers to symmetry in physical space, while intrinsic parity refers to symmetry in internal space. This means that while an object may exhibit spatial parity, it may not have intrinsic parity and vice versa.

How are spatial and intrinsic parity related?

Spatial and intrinsic parity are related in that they both involve the concept of symmetry. However, they are different types of symmetry and are not always present in the same object or system. Some objects may have both spatial and intrinsic parity, while others may only have one or the other.

Why is understanding spatial and intrinsic parity important?

Understanding spatial and intrinsic parity is important in many fields of science, including physics, chemistry, and biology. It allows scientists to predict and understand the behavior of objects and systems based on their symmetries, and has implications for various applications such as drug development and materials science.

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