Provide the equation for a system where the energy of an atom or molecule does not change with time.

The uncertainty in the position of an electron is $1 \, \mathring{A}$. Find the uncertainty in its velocity.

Given below are two statements $:$
Statement $(I):$ It is impossible to specify simultaneously with arbitrary precision,both the linear momentum and the position of a particle.
Statement $(II) :$ If the uncertainty in the measurement of position and uncertainty in measurement of momentum are equal for an electron,then the uncertainty in the measurement of velocity is $\geq \sqrt{\frac{h}{4\pi}} \times \frac{1}{m}$ which simplifies to $\geq \frac{1}{2m} \sqrt{\frac{h}{\pi}}$. In the light of the above statements,choose the correct answer from the options given below $:$

What does the uncertainty principle state regarding the existence of a definite path or trajectory of an electron?

What is the nature of the solution to the $Schrodinger$ wave equation for multi-electron atoms? How is it handled?

The uncertainty in the velocities of two particles $A$ and $B$ are $0.03 \ m \ s^{-1}$ and $0.01 \ m \ s^{-1}$ respectively. The mass of $B$ is four times the mass of $A$. The ratio of uncertainties in their positions is