As an example of the use of the Green's function method, we calculate the pressure exerted by a Gaussian chain on the walls of a confining box .

The potential is zero everywhere inside the box, and infinite everywhere
outside the box. Then
at the walls of the box. Solving Eq. (3.18)
yields

(3.21) |

(3.22) |

where

The partition function then reads

Z |
= | (3.25) | |

Z_{i} |
= | (3.26) |

Introducing the eigenfunctions and eigenvalues from Eqs. (3.23) and (3.24) we get

(3.27) |

where the prime at the summation sign indicates that only odd

Now look at two limits

*i.*-

The polymer is much smaller than the box

*Z*_{i}= (3.28) *Z*= (3.29)

The pressure on wall one is

(3.30)

i.e. independent of the wall number, and equal to the ideal gas result. *ii.*-

The polymer is very much constrained by the box

(3.31)

*P*_{1}= (3.32) = (3.33)

In this case the pressure on the different walls depends on the size of the box orthogonal to the wall.