Advanced — Potential WellHardQuestion 30475
Question
A particle in a 1D potential U(x) = x⁴ − 4x². The stable equilibrium positions are at:
- Ax = 0
- Bx = ±√2Correct
- Cx = ±2
- Dx = ±1
Correct answer
x = ±√2
Explanation
F = −dU/dx = −(4x³−8x) = 0 → x(4x²−8) = 0 → x=0 or x=±√2. U''(x) = 12x²−8. At x=±√2: U'' = 24−8 = 16 > 0 → stable. At x=0: U'' = −8 < 0 → unstable.