What does the angular momentum operator L(z)(hat) equal?
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What does the angular momentum operator L(z)(hat) equal?
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- Can you elaborate on the dirac notation for the raising and lowering operators. I am not understanding how you got (6n^2+6n+3)Show the relation LxL = iħL for the quantum mechanical angular momentum operator LIn the following potential well there are 2 non-interacting electrons with the same spin. If it is known that this is at the lowest energy, what is the wave function of this 2-particle system? ∞ , x a
- Discuss how the Hamiltonian operator for the hydrogen atom was constructed.Rewrite S₁ S₂ in terms of S², |S₁|², 5₂|² by using the identity |S² = |S₁ + S₂|² = |S₁|² + |5₂|² +25₁ · 5₂. Use this to show that the combined spin angular momentum basis 5² for the electron and proton spins is an eigenstate basis for this dipole interaction.The wave function for the ground state of hydrogen is given by 100(0,0) = Ae¯¯r/ª Find the constant A that will normalize this wave func- tion over all space.
- Consider three noninteracting indistinguishable spin-0 particles trapped in a harmonic potential with energy states given as: [nx, Ny, nz). Consider three distinct single particle states: |0,0,0), |0,1,0), |0,2,0). Each of the particles can be in any one of the three states listed. How many different three particle states are possible?We have a three dimensional vector space where |P1), |P2) and |23) form a complete orthonormal basis. In this vector space we have two states |a)=5i|1)+3i 2)+(-2+2i) 3) and |B) =4i|1)-5 i) Calculate (a and (B, in terms of the dual basis vectors (y|, (p2|, (P3|. ii) Calculate the inner/scalar products (alB) and (Ba). Show that (8|a) =(a|B)".