What are the units of Lz and L^2?

  • Thread starter smileandbehappy
  • Start date
  • Tags
    Units
In summary, the conversation discusses finding the total energy, Lz, and L^2 given quantum numbers n=2, l=1, m=-1. The equations used are E = -Er/n^2, Lz = mh(bar), and L^2 = l(l+1)(hbar)^2. The total energy is -3.4eV, Lz is -hbar, and L^2 is 2(hbar)^2. The units for angular momentum are J⋅s, the same as Plank's constant (h). The conversation also mentions using hbar instead of h for the calculations.
  • #1
smileandbehappy
66
0

Homework Statement



From quantum numbers: n=2, l=1, m=-1 find the total energy, Lz and L^2?

Homework Equations



E = -Er/n^2 (I think, although it refers to the total energy we have the principle quantum numbers so I'm good to go.

Lz = mh(bar)

L^2= l(L+1)(hbar)^2

The Attempt at a Solution


[/B]
E = -3.4eV (Just from plugging numbers)

Lz = - hbar

L^2 = 2(hbar)^2

(apologies for hbar - I don't know how to write it nicely. It's just planks constant divieded by 2pi)

However I can't find units for the Lz, or the L^2. Am I being incredibly stupid, and it the hbar the unit - or is there is there a uni? I have searched on hyperphysics and in three textbooks for this - and none give a unit, or a justification as to why there is now one.

Thanks.
 
Physics news on Phys.org
  • #2
smileandbehappy said:

Homework Statement



From quantum numbers: n=2, l=1, m=-1 find the total energy, Lz and L^2?

Homework Equations



E = -Er/n^2 (I think, although it refers to the total energy we have the principle quantum numbers so I'm good to go.

Lz = mh(bar)

L^2= l(l+1)(hbar)^2

The Attempt at a Solution


[/B]
E = -3.4eV (Just from plugging numbers)

Lz = - hbar

L^2 = 2(hbar)^2

(apologies for hbar - I don't know how to write it nicely. It's just planks constant divieded by 2pi)

However I can't find units for the Lz, or the L^2. Am I being incredibly stupid, and it the hbar the unit - or is there is there a uni? I have searched on hyperphysics and in three textbooks for this - and none give a unit, or a justification as to why there is now one.

Thanks.
What do L and Lz represent ? -- angular momentum and the z component of angular momentum ?

What are units for angular momentum?

Google Plank's constant. Here's a link to Wikipedia: http://en.wikipedia.org/wiki/Planck_constant

Units for ħ : Energy unit × time unit : J⋅s .

ħ has same units as h, Plank's constant.
 
  • #3
Ah thanks - I thought that hbar had something to do with the units - I'm just having a bad brain day.

The logical step here is to leave the answer in terms of hbar... but I'm not sure if that is what they want. I might just write it both ways to satisfy them.

Thanks
 

FAQ: What are the units of Lz and L^2?

What is the unit of Lz?

The unit of Lz, or the z-component of angular momentum, is typically measured in units of joule-seconds (J-s) or more commonly, Planck's constant (h).

What is the unit of L^2?

L^2, or the squared total angular momentum, is dimensionless and does not have a specific unit. It is often represented as a multiple of h^2 (h-bar squared).

How are Lz and L^2 related?

Lz and L^2 are related by the following equation: L^2 = Lx^2 + Ly^2 + Lz^2, where Lx and Ly are the x and y components of angular momentum. This equation shows that L^2 is the sum of the squared individual components of angular momentum.

Can Lz and L^2 have different units?

Yes, Lz and L^2 can have different units. Lz is typically measured in units of J-s or h, while L^2 is dimensionless and often represented as h^2. However, both Lz and L^2 are related to Planck's constant (h) and can be converted into each other using h.

How are Lz and L^2 used in quantum mechanics?

Lz and L^2 are important operators in quantum mechanics that describe the angular momentum of a particle in a particular direction. They are used to calculate the energy levels and wave functions of quantum systems, as well as to understand the behavior of particles in magnetic fields and other physical phenomena.

Back
Top