Understanding Brownian Motion with Weiner Integral and Delta Functions

[tpm]

HI, i would need some help to solve the Brownian motion given by the Weiner Integral(over paths):

$$\int \mathcal D [x_{t}]exp(-\int dt (m/2(\dot x)^{2}-V(x))$$

for the case $$V(x)=\delta (x) +\delta (x-1)+\delta (x-2)$$

any help would be appreciated, thanks

 

[lalbatros]

What do you mean by that: "solve the Brownian motion" ?

 

[Jason Swanson]

HI, i would need some help to solve the Brownian motion given by the Weiner Integral(over paths):

$$\int \mathcal D [x_{t}]exp(-\int dt (m/2(\dot x)^{2}-V(x))$$

for the case $$V(x)=\delta (x) +\delta (x-1)+\delta (x-2)$$

any help would be appreciated, thanks

Can you please explain your notation? In particular, what is $$x_t$$, what is $$\dot x$$, and what is $$\mathcal D$$?