[열 물리학 11] Probability(확률 ), Ensemble (앙상블)

Probability

we have a closed system the we know is equally likely to be in any of the g accessible quantum states.

 

generalstate label.

 

The probability P(s) of finding the system in this state is

if the state s is accessible and p(s)=0 otherwise, consistent with the fundamental assumption.

 

The sum

of Probability over all states is always equal to unity, because the total Probability that the system is in some state is unity:

definition of the average

suppose that the physical property X has the value X(s) when the system is in the state s.

 

Here X 는 나타낼 수 있습니다. magentic moment, energy, square of the energy, charge density near a point

 r (벡터)  , or any property that can be observed when the system is in a quantum state

 

 

Then the average of the observations of the quantity X taken over a system described by the probabilities P(s) is

For a closed system, average value of X is

 

<X>를 ensemble average 라고 부른다.

ex) g개의 similar systems을 생각해보자, one in each accessible(허용된) quantum state. such a group of systems constructed alike is called an ensemble of systems (비슷한 system의 모임을 system ensemble )

 

집합체의 평균을 ensemble average 이라고 한다.

->The average of any property over the group is called the ensemble average of that property

 

 

 

 

 

 

 

 

Ensemble(앙상블)

 

An ensemble of systems is composed many system, all constructed alike.

->Each system in the ensemble is a replica(복제품) of the actual system in one of the quantum states accessible to the system 

 

(ex 1) For spin system N=10

u=-2smB = -8mB -> 2s =8

출처:kittle 열 물리학

 

인 상황 a ,b, c, d, ..., j 각 줄들을 ensemble 하나씩이다.

(=replica of the actual system)

 

 

(ex2) For N=5 2s =1

 

 

 

(ex3) For N=5, 2s=5