iℏ |
∂ -- ∂t |
Ψ(r,t) | = | Ĥ Ψ(r,t) | (equation 17) |
iℏ |
∂ -- ∂t |
Ψ(r,t) | = | - |
ℏ^{2} -- 2m | Δ Ψ(r,t) | + | V(r) Ψ(r,t) | (equation 18) |
E_{N} Ψ_{N}(x) | = |
ℏ^{2} ∂^{2} -------- 2m ∂ x^{2} |
Ψ_{N}(x) | (equation 19) |
∂^{2} --- ∂ x^{2} |
Ψ_{N}(x) | + | k_{N}^{2} Ψ_{N}(x) | = 0 | (equation 20) |
|B > | = |
┌ b_{1} ┐ │ b_{2} │ └ b_{3} ┘ |
< A|B > | = | [a^{*}_{1},a^{*}_{2},a^{*}_{3}] | · |
┌ b_{1} ┐ │ b_{2} │ └ b_{3} ┘ | = | a^{*}_{1}b_{1} + a^{*}_{2}b_{2} + a^{*}_{3}b_{3} |
┌ a_{11} a_{12} a_{13} ┐ │ a_{21} a_{22} a_{23} │ └ a_{31} a_{32} a_{33}┘ |
┌ B_{1} ┐ │ B_{2} │ └ B_{3} ┘ |
= |
┌ a_{11}*B_{1}+a_{12}*B_{2}+a_{13}*B_{3} ┐ │ a_{21}*B_{1}+a_{22}*B_{2}+a_{23}*B_{3} │ └ a_{31}*B_{1}+a_{32}*B_{2}+a_{33}*B_{3} ┘ |
= |
┌ C_{1} ┐ │ C_{2} │ └ C_{3} ┘ |
[ A_{1} A_{2} A_{3} ] |
┌ a_{11} a_{12} a_{13} ┐ │ a_{21} a_{22} a_{23} │ └ a_{31} a_{32} a_{33} ┘ |
= | [ C_{1} C_{2} C_{3} ] |
|B > < A| | = |
┌ B_{1} ┐ │ B_{2} │ └ B_{3} ┘ |
[ A_{1}^{*} A_{2}^{*} A_{3}^{*} ] | = |
┌ B_{1}A_{1}^{*}+B_{1}A_{2}^{*}+B_{1}A_{3}^{*} ┐ │ B_{2}A_{1}^{*}+B_{2}A_{2}^{*}+B_{2}A_{3}^{*} │ └ B_{3}A_{1}^{*}+B_{3}A_{2}^{*}+B_{3}A_{3}^{*} ┘ |
┌ ½ 0 ┐ └ 0 ½ ┘ |
|φ> | = |
┌ a_{1} ┐ │ a_{2} │ └ a_{3} ┘ |
┌ 0 0 0 ┐ │ 0 0 0 │ └ 0 0 1 ┘ |
O|φ> | = |
┌ 0 0 0 ┐ │ 0 0 0 │ └ 0 0 1 ┘ |
┌ a_{1} ┐ │ a_{2} │ └ a_{3} ┘ |
= |
┌ 0_{ } ┐ │ 0_{ } │ └ a_{3}┘ |
[a^{*}_{1},a^{*}_{2},a^{*}_{3}] | · |
┌ a_{11} 0 0 ┐ │ 0 a_{22} 0 │ └ 0 0 a_{33} ┘ |
· |
┌ a_{1} ┐ │ a_{2} │ └ a_{3} ┘ |
= (a^{*}_{1}a_{1}) a_{11} + (a^{*}_{2}a_{2}) a_{22} + (a^{*}_{3}a_{3}) a_{33} |
┌ 1 ┐ │ 0 │ └ 0 ┘ |
, |
┌ 0 ┐ │ 1 │ └ 0 ┘ |
, |
┌ 0 ┐ │ 0 │ └ 1 ┘ |
┌ a b c ┐ │ d e f │ └ g h i ┘ |
┌ 1 ┐ │ 0 │ └ 0 ┘ |
= |
┌ a*1+b*0+c*0 ┐ │ d*1+e*0+f*0 │ └ g*1+h*0+i*0 ┘ |
= |
┌ a ┐ │ d │ └ g ┘ |
┌ 1 ┐ │ 0 │ └ 0 ┘ |
┌ a ┐ │ d │ └ g ┘ |
= | a |
┌ 1 0┐ └ 0 1┘ |
= | |i > < i| + |j > < j| | = I |
A = |
┌ 0 -i┐ └ i 0 ┘ |