- #1
zexxa
- 32
- 7
Question
Form the canoncial partition using the following conditions:
Attempt
I treated the energy states at ##i /leq m## and ## i > m## as a simple one energy state i.e.
## E = \sum_i ^N n_i \epsilon , {n_i} = \begin{cases} 1, & \text{if $i \leq m$}.\\
0, & \text{otherwise} \end{cases}##
Therefore,
##Z(\beta , V , N) = \{ exp[ - \beta \epsilon ] \} ^m \{ exp[ 0 ]\} ^{N-m} = exp[ - \beta \epsilon ] ^m##
Does this make sense?
Form the canoncial partition using the following conditions:
- 2 N-particles long strands can join each other at the i-th particle to form a double helix chain.
- Otherwise, the i-th particle of each strand can also be left unattached, leaving the chain "open"
- An "open" link gives the strand ##\epsilon## amount of energy where ##\epsilon > 0##
- A "closed" link gives the strand no energy
- For ##m < N##, the strand must be "open" for ##i \leq m## and "closed" for ##m < i \leq N##
- Note that ##m \neq N##
- Each particle are independent of each other and they weakly interact
Attempt
I treated the energy states at ##i /leq m## and ## i > m## as a simple one energy state i.e.
## E = \sum_i ^N n_i \epsilon , {n_i} = \begin{cases} 1, & \text{if $i \leq m$}.\\
0, & \text{otherwise} \end{cases}##
Therefore,
##Z(\beta , V , N) = \{ exp[ - \beta \epsilon ] \} ^m \{ exp[ 0 ]\} ^{N-m} = exp[ - \beta \epsilon ] ^m##
Does this make sense?