Calculating Total Energy for 1-d Electron Gas

[mblaskovic]

HI!

Also:

I have 1-d electron gas in tight banding model with included interaction between electrons of same spins V_{\uparrow}=-N_{\uparrow}U where U > 0, \sigma=\pm1 is spin up or down, and pauli interaction with outside field B is included. I have to calculate the total energy of gas at T=0K as function of of polarization x=\frac{N_{\uparrow}-N_{\downarrow}}{N} expand it to series up to 6th order, minimize it and find the nontrivial solution for U N=N_{\uparrow}+N_{\downarrow}, N_{\uparrow}=\frac{N}{2}(1+x)
and N_{\downarrow}=\frac{N}{2}(1-x)
N_{\sigma}=\frac{N}{2}(1+{\sigma}x)
my major problem is calculating the total energy

 

[mblaskovic]

HI!

My problem is next:

I have 2-d electron gas with included interaction between electrons of opposite spins V_{\sigma}=N_{\sigma}U where U > 0 and \sigma=\pm1 is spin up or down, and pauli interaction with outside field B is included. I have to calculate the total energy of gas at T=0K as function of N_{\sigma}, then i have to minimize the energy as function of polarization parameter x=\frac{N_{\uparrow}-N_{\downarrow}}{N} and calculate the suscepitibility

N=N_{\uparrow}+N_{\downarrow}, N_{\uparrow}=\frac{N}{2}(1+x), N_{\downarrow}=\frac{N}{2}(1-x), and N_{\sigma}=\frac{N}{2}(1+{\sigma}x)

my major problem is calculating the total energy, the rest is not so tough i am just not sure that my energy is calculated correct...