If I temporarily get rid of the uncertainty introduced by Manipulate and NIntegrate, put all the terms inside your NIntegrate into a list, ignore that the second NIntegrate is in the denominator which will only introduce more denominators, separate all the terms with commas, try to choose reasonable starting conditions and display the values of those terms then the error messages tell me you have LOTS of zero denominators.

In[1]:= w = 1.88*10^11;

h = 1.054571726*10^-34;

m = .063 9.11 10^-31;

Vz = .05;

Vp = .05;

Vd = 0;

kp = 0;

kz = 0;

{h/(2 m), kz^2 kp (kz^2 (Vz) + kp^2 (Vp))^(-1/2), (1/(kz^2 + kp^2)),

Exp[-1/8 ((h (kp^2 + kz^2)/(2 m) - kz Vd + w)^2/(kz^2 + kp^2))],

Exp[-1/8 ((h (kp^2 + kz^2)/(2 m) + kz Vd + w)^2/(kz^2 + kp^2))],

Coth[1/2.] + 1,

Exp[-1/8 ((h (kp^2 + kz^2)/(2 m) - kz Vd - w)^2/(kz^2 + kp^2))],

Exp[-1/8 ((h (kp^2 + kz^2)/(2 m) + kz Vd - w)^2/(kz^2 + kp^2))],

Coth[1/2.] - 1,

kz^2 kp (kz^2 (Vz) + kp^2 (Vp))^(-3/2),

(1/(kz^2 + kp^2)),

h (kp^2 + kz^2)/(2 m),

kz Vd + w,

Exp[-1/8 ((h (kp^2 + kz^2)/(2 m) - kz Vd + w)^2/(kz^2 + kp^2))],

(h (kp^2 + kz^2)/(2 m) + kz Vd + w),

Exp[-1/8 ((h (kp^2 + kz^2)/(2 m) + kz Vd + w)^2/(kz^2 + kp^2))],

(Coth[1/2.] + 1),

(h (kp^2 + kz^2)/(2 m) - kz Vd - w),

Exp[-1/8 ((h (kp^2 + kz^2)/(2 m) - kz Vd - w)^2/(kz^2 + kp^2))],

(h (kp^2 + kz^2)/(2 m) + kz Vd - w),

Exp[-1/8 ((h (kp^2 + kz^2)/(2 m) + kz Vd - w)^2/(kz^2 + kp^2))],

(Coth[1/2.] - 1)}

During evaluation of In[1]:= Power::infy: Infinite expression 1/Sqrt[0.] encountered. >>

During evaluation of In[1]:= Infinity::indet: Indeterminate expression 0 ComplexInfinity encountered. >>

During evaluation of In[1]:= Power::infy: Infinite expression 1/0 encountered. >>

During evaluation of In[1]:= Power::infy: Infinite expression 1/0 encountered. >>

During evaluation of In[1]:= General::stop: Further output of Power::infy will be suppressed during this calculation. >>

During evaluation of In[1]:= Infinity::indet: Indeterminate expression E^ComplexInfinity encountered. >>

During evaluation of In[1]:= Infinity::indet: Indeterminate expression E^ComplexInfinity encountered. >>

During evaluation of In[1]:= General::stop: Further output of Infinity::indet will be suppressed during this calculation. >>

Out[9]= {0.000918729, Indeterminate, ComplexInfinity, Indeterminate,

Indeterminate, 3.16395, Indeterminate, Indeterminate, 1.16395,

Indeterminate, ComplexInfinity, 0., 1.88*10^11, Indeterminate,

1.88*10^11, Indeterminate, 3.16395, -1.88*10^11, Indeterminate,

-1.88*10^11, Indeterminate, 1.16395}

In that you have kp=0 and kz=0 and you have lots of demoninators of kz^2+kp^2.

Arbitrarily make kp=1 and kz=1 and see if that fixes the problem.

In[49]:= w = 1.88*10^11;

h = 1.054571726*10^-34;

m = .063 9.11 10^-31;

Vz = .05;

Vp = .05;

Vd = 0;

kp = 1;

kz = 1;

{h/(2 m), kz^2 kp (kz^2 (Vz) + kp^2 (Vp))^(-1/2),

(1/(kz^2 + kp^2)),

Exp[-1/8 ((h (kp^2 + kz^2)/(2 m) - kz Vd + w)^2/(kz^2 + kp^2))],

Exp[-1/8 ((h (kp^2 + kz^2)/(2 m) + kz Vd + w)^2/(kz^2 + kp^2))],

Coth[1/2.] + 1,

Exp[-1/8 ((h (kp^2 + kz^2)/(2 m) - kz Vd - w)^2/(kz^2 + kp^2))],

Exp[-1/8 ((h (kp^2 + kz^2)/(2 m) + kz Vd - w)^2/(kz^2 + kp^2))],

Coth[1/2.] - 1,

kz^2 kp (kz^2 (Vz) + kp^2 (Vp))^(-3/2),

(1/(kz^2 + kp^2)),

h (kp^2 + kz^2)/(2 m),

kz Vd + w,

Exp[-1/8 ((h (kp^2 + kz^2)/(2 m) - kz Vd + w)^2/(kz^2 + kp^2))],

(h (kp^2 + kz^2)/(2 m) + kz Vd + w),

Exp[-1/8 ((h (kp^2 + kz^2)/(2 m) + kz Vd + w)^2/(kz^2 + kp^2))],

(Coth[1/2.] + 1),

(h (kp^2 + kz^2)/(2 m) - kz Vd - w) ,

Exp[-1/8 ((h (kp^2 + kz^2)/(2 m) - kz Vd - w)^2/(kz^2 + kp^2))],

(h (kp^2 + kz^2)/(2 m) + kz Vd - w) ,

Exp[-1/8 ((h (kp^2 + kz^2)/(2 m) + kz Vd - w)^2/(kz^2 + kp^2))],

(Coth[1/2.] - 1)}

During evaluation of In[49]:= General::unfl: Underflow occurred in computation. >>

During evaluation of In[49]:= General::unfl: Underflow occurred in computation. >>

During evaluation of In[49]:= General::unfl: Underflow occurred in computation. >>

During evaluation of In[49]:= General::stop: Further output of General::unfl will be suppressed during this calculation. >>

Out[57]= {0.000918729, 3.16228, 1/2, Underflow[], Underflow[], 3.16395, Underflow[],

Underflow[], 1.16395, 31.6228, 1/2, 0.00183746, 1.88*10^11,

Underflow[], 1.88*10^11, Underflow[], 3.16395, -1.88*10^11,

Underflow[], -1.88*10^11, Underflow[], 1.16395}

Mathematica has a method of keeping track of the precision of every result. If you give a constant with a single digit after the decimal point it then the result of every calculation using that constant will only have a single good known digit after the decimal point. (Actually that isn't really precisely true, no pun intended, but the really precisely true answer is probably something you don't want to know). So let's see if we can fool it by claiming we have about 20 good known digits after every one of the decimal points.

In[58]:= w = 1.88000000000000000000*10^11;

h = 1.054571726000000000000000000*10^-34;

m = .063000000000000000000 9.11000000000000000000 10^-31;

Vz = .05000000000000000000;

Vp = .05000000000000000000;

Vd = 0;

kp = 1;

kz = 1;

{h/(2 m) , kz^2 kp (kz^2 (Vz) + kp^2 (Vp))^(-1/2),

(1/(kz^2 + kp^2)),

Exp[-1/8 ((h (kp^2 + kz^2)/(2 m) - kz Vd + w)^2/(kz^2 + kp^2))],

Exp[-1/8 ((h (kp^2 + kz^2)/(2 m) + kz Vd + w)^2/(kz^2 + kp^2))],

Coth[1/2.000000000000000000] + 1,

Exp[-1/8 ((h (kp^2 + kz^2)/(2 m) - kz Vd - w)^2/(kz^2 + kp^2))],

Exp[-1/8 ((h (kp^2 + kz^2)/(2 m) + kz Vd - w)^2/(kz^2 + kp^2))],

Coth[1/2.000000000000000000] - 1,

kz^2 kp (kz^2 (Vz) + kp^2 (Vp))^(-3/2),

(1/(kz^2 + kp^2)),

h (kp^2 + kz^2)/(2 m),

kz Vd + w,

Exp[-1/8 ((h (kp^2 + kz^2)/(2 m) - kz Vd + w)^2/(kz^2 + kp^2))],

(h (kp^2 + kz^2)/(2 m) + kz Vd + w),

Exp[-1/8 ((h (kp^2 + kz^2)/(2 m) + kz Vd + w)^2/(kz^2 + kp^2))],

(Coth[1/2.000000000000000000] + 1),

(h (kp^2 + kz^2)/(2 m) - kz Vd - w),

Exp[-1/8 ((h (kp^2 + kz^2)/(2 m) - kz Vd - w)^2/(kz^2 + kp^2))],

(h (kp^2 + kz^2)/(2 m) + kz Vd - w) ,

Exp[-1/8 ((h (kp^2 + kz^2)/(2 m) + kz Vd - w)^2/(kz^2 + kp^2))],

(Coth[1/2.000000000000000000] - 1)}

During evaluation of In[58]:= General::unfl: Underflow occurred in computation. >>

During evaluation of In[58]:= General::unfl: Underflow occurred in computation. >>

During evaluation of In[58]:= General::unfl: Underflow occurred in computation. >>

During evaluation of In[58]:= General::stop: Further output of General::unfl will be suppressed during this calculation. >>

Out[66]= {0.0009187285261268795846, 3.162277660168379332, 1/2,

Underflow[], Underflow[], 3.16395341373865285, Underflow[],

Underflow[], 1.16395341373865285, 31.62277660168379332, 1/2,

0.0018374570522537591692, 1.8800000000000000000*10^11, Underflow[],

1.8800000000000183746*10^11, Underflow[], 3.16395341373865285,

-1.8799999999999816254*10^11, Underflow[], -1.8799999999999816254*10^11,

Underflow[], 1.16395341373865285}

So even increased accuracy doesn't fix the problem. And adding NIntegrate with its precision issues will only compound this.

So what I believe happened was the crash ate part of your code or part of the code wasn't saved before the crash

and the problem is that you have lots of denominators that are either zero and that you have very large negative

and positive exponents in constants and couple that with the Exp function and that that you have negative exponents,

all this is giving you lots of zeros in denominators.

If you make all those go away or you carefully analyze the code and manage all the accuracy issues then I suspect

that will correct the first wave of problems with the code.