null
US
Entrar
Registre-se gratuitamente
Registre-se
Detectamos que o JavaScript não está habilitado no teu navegador. Habilite o Javascript para o funcionamento correto do nosso site. Por favor, leia os
Termos e Condições
para mais informações.
Próximo
Copiar e Editar
Você deve estar logado para concluir esta ação!
Inscreva-se gratuitamente
710078
Quantum Mechanics II
Descrição
Mapa Mental sobre Quantum Mechanics II, criado por franz.sciortino em 02-04-2014.
Mapa Mental por
franz.sciortino
, atualizado more than 1 year ago
Mais
Menos
Criado por
franz.sciortino
mais de 10 anos atrás
55
2
0
Resumo de Recurso
Quantum Mechanics II
Ladder operators (not Hermitian) are "empirically" found to raise/lower energy states
Very useful: [H, a]= - h_bar *w*a and [H, a']=h_bar*w*a'
Use condition a*u_0=0 to find momentum eigenstates and multiply by a' to find energy eigenstates
Some results are representation-independent
Time-independent Perturbation Theory
find variation in eigenvalues by setting (u_n)'= u_n
Find eigenstates by letting (E_n)'=E_n and ignoring 2nd order terms
Degeneracy
Generally produced by symmetries
Individual states might not exhibit symmetry, but sums of prob. densities must always do
Superpositions of eigenstates are still eigenstates
Schmidt orthogonalization: procedure to make degenerate states orthogonal (always possible)
With degeneracy, if two operators commute, then there always exists a combination of them which is compatible
Orbital angular momentum
L_i components are given by (r x p)
In cyclic order, [Lx, Ly]= i h_bar *Lz
L^2 commutes with L_i components, but these do not commute between themselves
We can write eigenvalue equations: L^2 Y = alpha Y and L_z Y = beta Y
Define ladder operators L+ and L- to show many ang.momentum rotations for each length
Use conditions of ladder operators to find eigenvalues: alpha=l(l+1) h_bar and beta= m_l h_bar
Find ang. momentum eigenstates using L_z and L^2 spherical components --> Legendre equations --> spherical harmonics
Central potentials give [H, L^2]=0 (conservation of ang.mom.)
Obtain radial equation from TISE with central potential barrier and separation of variables
Measuring ang.mom. experiments: Zeeman, Stern-Gerlach, Uhlenbeck-Goudsmit spin proposition
Spin angular momentum
Analogies with orbital ang.mom. postulated, but only 2 states allowed
Knowing needed eigenvalues, deduce eigenstates (matrices)
Pauli matrices, up/down spin states
Find shifts in energies in uniform magnetic fields by mu_B *B
Larmor precession of S_x and S_y, with constant S_z over time
Quer criar seus próprios
Mapas Mentais
gratuitos
com a GoConqr?
Saiba mais
.
Semelhante
NA CONSTITUIÇÃO - Princípios Gerais
daniel_cal
Terminologia Cirúrgica
lion.elsuffi
English - prepositions (at, in, on)
jdbenthien
Leitura para o First Certificate (I)
GoConqr suporte .
CAE - Cambridge Advanced: English
Luiz Fernando
Questões - Lei 8112/90
Lucas Ávila
Ligações Intermoleculares
GoConqr suporte .
Direito Previdenciário INSS 2015
André Cavallini
Técnicas de Estudo para Melhorar sua Aprendizagem
GoConqr suporte .
5 Ferramentas de Estudo para Melhorar sua Aprendizagem -Vestibular e Enem
GoConqr suporte .
Normas, princípios e regras
Rafael Ferreira da Silva
Explore a Biblioteca