Use Uncertainty principle to find gound state energy?

AI Thread Summary
The discussion revolves around using the uncertainty principle to estimate the ground state energy of a particle subjected to a linear potential V(x)=Kx. Participants suggest following an example from a quantum mechanics resource that demonstrates a similar approach. There is a request for guidance on finding relevant examples in textbooks that may assist in solving the problem. The conversation highlights the need for a clear application of the uncertainty principle in this context. Overall, the thread emphasizes the importance of referencing established examples to tackle complex quantum mechanics problems.
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Homework Statement


A particle of mass m is subjected to a potential V(x)=Kx.Use uncertainty principle in the form Δx.Δp≈h(bar)/2 to estimate ground state energy of the particle.

The Attempt at a Solution


I have no idea. :(
 
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Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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