State evolution in finite suden-broading quantum well

[Guangwei Yuan]

suppose we have a single eigen-state finite potential well like following:
V(x)= V, x<-a and x>a;
0, -a<=x<=a;
say only one eigen-state within this well S1(x)

when all of sudden this potetial well broden by size of 2
V(x)= V, x<-2a and x>2a;
0, -2a<=x<=2a;
say still only one eigen-state within this new well S1(x)

Please give a suggestion how long as t as the state from S0(x) changes to S1(x). Thanks in advance. Have a nice day.

[chasingwind]

Yuan, you can try to look for the answer to this problem in Zeng jinyan and Qian bochu's exercises' book on Quantum Mechanics. I think it has the same exercise. Good luck!