- #1
A_B
- 93
- 1
halfway page 41 Bohm obtains for the action variable
[tex]
J = 2\int_{a(E)}^{b(E)} dq \sqrt{2m[E-V(q)]}
[/tex]
Then he obtians the partial derivative to E "by a well-known theorem of the calculus":
[tex]
\frac{\partial J}{\partial E} = 2\left\{ \sqrt{2m\left[E-V(q)\right]} \right\}_{q=b} \frac{\partial b}{\partial E} - 2\left\{ \sqrt{2m[E-V(q)]} \right\}_{q=a} \frac{\partial a}{\partial E} + 2 \int_a^b \sqrt{\frac{m}{2[E-V(q)]}} dq.
[/tex]
What is this "well-known theorem"?
Thanks,
A_B
[tex]
J = 2\int_{a(E)}^{b(E)} dq \sqrt{2m[E-V(q)]}
[/tex]
Then he obtians the partial derivative to E "by a well-known theorem of the calculus":
[tex]
\frac{\partial J}{\partial E} = 2\left\{ \sqrt{2m\left[E-V(q)\right]} \right\}_{q=b} \frac{\partial b}{\partial E} - 2\left\{ \sqrt{2m[E-V(q)]} \right\}_{q=a} \frac{\partial a}{\partial E} + 2 \int_a^b \sqrt{\frac{m}{2[E-V(q)]}} dq.
[/tex]
What is this "well-known theorem"?
Thanks,
A_B