*Problem 1.9

$$\Psi(x,t) = Ae^{ -a\left[\frac{mx^{2}}{\hbar}+it\right]}$$

Question

*Problem 1.9

$$\Psi(x,t) = Ae^{ -a\left[\frac{mx^{2}}{\hbar}+it\right]}$$

unklerhaukus · Answer

attachment

unklerhaukus · Answer

attachment

unklerhaukus · Answer

what can we make of the result


$$\sigma_x\sigma_p=\sqrt{\frac \hbar {4am}}\sqrt{am\hbar}=\frac \hbar2$$

mathslover · Answer

What can i give you is just.... @mukushla and @Xishem (may like to try this)

anonymous · Answer

But do we need any knowledge of physics to solve this?

unklerhaukus · Answer

all the physics you need to know is          i=√-1

mathslover · Answer

where i = iota 

i is an imaginary number ...

cruffo · Answer

Wait a minute...Heisenberg inequalities
$$\sigma_x\sigma_p \geq \frac{\hbar}{2}$$
So the result would be consistent.  But what's the significance of equality?

cruffo · Answer

Would equality mean that the particle is a perfect Gaussian, and therefore can be located in spacetime and conjugate momentum space, down to exactly $\frac{\hbar}{2}$?  So, in a since, very little uncertainty in the measurements of position and momentum?