Finding stationary points and TS barriers for U(x,y)=A sin(πx/Lx)+B cos(πy/Ly)

[adam1]

U(x,y)=Asin(pi*x/Lx) + Bcos(pi*y/Ly) where A,B,Lx,Ly are positive

1 Locate all the stationary points (i.e. minima, maxima and transition states
(TS)) for this potential.

a. What is the periodicity of U(x,y) along the two directions?

b. Derive the TS barriers that an atom diffusing on the surface would
have to surmount during a “jump” between two minima as a function
of A and B.

c. Using information about the shape of U(x,y), propose possible
analytical curves separating the basin of attraction of adjacent minima.

 

[chaoseverlasting]

I don't know about the TS barrier or separating the basin of attraction, but the stationary points can be found by differentiating the equation, equating it to zero and finding the solution. The solutions are the stationary points.

For the periodicity, you can express the above function in a single term which takes into account both the trigonometric functions, and find the periodicity of that.