Total Possible Quantum States When n = 2

In summary, to find the total number of allowed states for a particle with a principal quantum number of n=2, we must consider the allowed orbital quantum numbers (l=0,1) and the number of allowed values of m_l for each (m_l=0 for l=0 and m_l=-1,0,1 for l=1). Adding these quantities together gives a total of 6, which when multiplied by 2 to account for spin orientations, gives a final answer of 12 possible quantum states.
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xinlan
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Homework Statement



The quantum state of a particle can be specified by giving a complete set of quantum numbers (n, l, m_s, m_l) . How many different quantum states are possible if the principal quantum number is n = 2?

To find the total number of allowed states, first write down the allowed orbital quantum numbers l, and then write down the number of allowed values of m_l for each orbital quantum number. Sum these quantities, and then multiply by 2 to account for the two possible orientations of spin.


Homework Equations





The Attempt at a Solution



since n = 2
then l = 0,1
m_l for l = 0 --> 0
m_l for l = 1 --> -1,0,1
then I added them up, which is 6
and then multiply it by 2, which is 12.

but I got wrong..
please help me..
thanks..
 
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  • #2
it's ok.. I got it.. :)
 
  • #3
can you show me?!
 

1. What is the total possible number of quantum states when n = 2?

There are four total possible quantum states when n = 2. These states are known as the ground state, excited state, superposition state, and entangled state.

2. How are these quantum states represented mathematically?

The quantum states when n = 2 are represented by the quantum numbers n, l, ml, and ms. These numbers describe the energy level, orbital type, orbital orientation, and spin orientation, respectively.

3. What is the significance of the ground state in quantum mechanics?

The ground state is the lowest energy state of a quantum system. It is considered to be the most stable state and serves as a reference point for comparing the energies of other states.

4. How is superposition state different from other quantum states?

The superposition state is unique in that it is a combination of two or more quantum states. This means that the system is in multiple states simultaneously, until it is measured and collapses into a single state.

5. Can two particles be in an entangled state when n = 2?

Yes, two particles can be in an entangled state when n = 2. This means that the particles are connected in such a way that the state of one particle cannot be described without considering the state of the other particle, even if they are physically separated.

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