plotting - particle motion in 1D anharmonic well

I have set of data points but I want to draw the trajectory of particle moving inside this well either in phase space. How can I do this? I tried with VectorPlot but not come out with good and set of data point are as follows: mass of particle is 10^-24 kg and here in this data first column is position & second potential. I am very thankful to you if you can help me to do this. Thank you.

x={2.*10^-6, 1.9*10^-6, 1.8*10^-6, 1.7*10^-6, 1.6*10^-6, 1.5*10^-6, 
     1.4*10^-6, 1.3*10^-6, 1.2*10^-6, 1.1*10^-6, 1.*10^-6, 9.*10^-7, 
     8.*10^-7, 7.*10^-7, 6.*10^-7, 5.*10^-7, 4.*10^-7, 3.*10^-7, 2.*10^-7,
      1.*10^-7, 0, -1.*10^-7, -2.*10^-7, -3.*10^-7, -4.*10^-7, -5.*10^-7, \
    -6.*10^-7, -7.*10^-7, -8.*10^-7, -9.*10^-7, -1.*10^-6, -1.1*10^-6, \
    -1.2*10^-6, -1.3*10^-6, -1.4*10^-6, -1.5*10^-6, -1.6*10^-6, \
    -1.7*10^-6, -1.8*10^-6, -1.9*10^-6, -2.*10^-6}  


 Vx = {-2.39203*10^-19, -2.38026*10^-19, -2.37166*10^-19, -2.36809*10^-19, \
-2.37117*10^-19, -2.38208*10^-19, -2.40143*10^-19, -2.42925*10^-19, \
-2.46503*10^-19, -2.50782*10^-19, -2.55644*10^-19, -2.60954*10^-19, \
-2.6657*10^-19, -2.72342*10^-19, -2.78094*10^-19, -2.83618*10^-19, \
-2.88644*10^-19, -2.92835*10^-19, -2.95779*10^-19, -2.97001*10^-19, \
-2.96*10^-19, -2.92287*10^-19, -2.8545*10^-19, -2.75213*10^-19, \
-2.61492*10^-19, -2.44433*10^-19, -2.24423*10^-19, -2.0208*10^-19, \
-1.782*10^-19, -1.53693*10^-19, -1.29492*10^-19, -1.06466*10^-19, \
-8.5334*10^-20, -6.6606*10^-20, -5.0546*10^-20, -3.7171*10^-20, \
-2.6278*10^-20, -1.75*10^-20, -1.0373*10^-20, -4.409*10^-21, 

 1.*10^-21}

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