about PSI purity

[jesusmontera]

Hello again, when running the example "1D_interactive_fermions" without potential (setting V=0 for both oscillator and coulomb), if I get the PSI purity it always return 0.5 (maximun entangled), when it must be 1, because if there is no potential particles can't be entagled. No matter the method I use, Crack or Split. If I initilize the psi with my own function(without potential and with kinetic move), it shows purity 1 like it must be. So what's going on?

def MyPsi2P(size, e1, e2, packetwidth, dt, barrierenergy, barrierwidth, initpos):
    psi = np.zeros((size,size),dtype=complex)
    centerX = math.floor(size*initpos)
    centerY = size - centerX		
    k1 = math.sqrt(2*e1)
    k2 = - math.sqrt(2*e2)
    pw = pow(packetwidth,2)
    for y in range (size):
        for x in range (size):                                        
            x0=x-centerX
            y0=y-centerY                
            envelope=math.exp(-(x0*x0+y0*y0) /pw)
            
            phasemoveReal=math.cos(k1*x0)*math.cos(k2*y0) - math.sin(k1*x0)*math.sin(k2*y0)
            phasemoveImag=math.cos(k1*x0)*math.sin(k2*y0) + math.sin(k1*x0)*math.cos(k2*y0);
            psi[y][x] = complex(envelope * phasemoveReal, envelope * phasemoveImag)
`
And her is the function that measures purity, (with psi reshaped to 1D):
```
def shcroduingerpurity(psi):

    size=int(len(psi)**0.5)    
    p=0
    #xMaxm1 = size - 1
    for xp in range(0,size,1):        
        for x in range(xp,size,1):
            rhore = 0.0	
            rhoim = 0.0	
            for y in range(0,size,1):                
                i1 = x + size*y;
                i2 = xp + size*y;
                rhore =rhore +  psi[i1].real * psi[i2].real + psi[i1].imag * psi[i2].imag
                rhoim = rhoim + psi[i1].real * psi[i2].imag - psi[i2].real*psi[i1].imag
            if x == xp:                
                p = p + rhore*rhore + rhoim*rhoim
            else:
                p = p + 2.*(rhore*rhore + rhoim*rhoim)	
            

    return p
```
```