# 행렬 역학

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## 개요

• correspondence principle

## 1

$$*_{mn}$$ 은 transition $$E_{m}\to E_{n}$$ 과 관계된 양들

$$Q=\left(q_{mn}e^{2\pi it\nu_{mn}}\right)$$

$$P=\left(p_{mn}e^{2\pi it\nu_{mn}}\right)$$

• 여기서 $$q_{mn},p_{mn}$$ : amplitudes, $$\nu_{mn}$$ : frequency 로 다음 조건을 만족시킴
• $$q_{mn}=q_{nm}^{*}$$
• $$p_{mn}=q_{nm}^{*}$$
• $$\nu_{mn}=-\nu_{nm}$$
• $$m \neq n$$ 이면, $$\nu_{mn}\neq 0$$
• $$\nu_{rs}+\nu_{st}=\nu_{rt}$$

## 2

• $$[Q,P] = Q P - P Q = i \hbar$$
• Born-Jordan condition 이라고도 불리며 보어-좀머펠트 양자 조건에 해당

## 3

• $$H(P,Q)$$ 해밀토니안

## 4

• 운동방정식
• $$\dot{Q}_i=\partial H/\partial P$$
• $$\dot{P}=-\partial H/\partial Q$$

$$H(P,Q)$$ 는 대각행렬이며, 고유값은 $$E_n$$

$$E_{m}-E_{n}=\hbar \nu_{mn}$$

## 메모

On the other hand, matrix mechanics was invented by Heisenberg in June 1925, and presented in a fully developed form in Dirac’s first paper on quantum mechanics (received 7 November 1925) and also in the famous “three-men’s paper” of Born, Heisenberg and Jordan (received 16 November 1925).