An Explanation of Mr. A’s Uncertainty Principle

Problem Statement

Are you familiar with the idea that "light is both a particle and a wave"? This is what Albert Einstein referred to as the "duality of light" (wave-particle duality).

In the realm of quantum mechanics, it is understood that not only light, but also objects like desks, the air around us, and even human beings, possess both particle-like and wave-like properties.

Consider a person named A—someone who is unhealthy, exceptionally prone to boredom, and detests sitting still. A lives a life much like a wild animal, unable to feel at ease unless constantly on the move.

Given A’s personality, a specific set of rules governs the relationship between the "space A is permitted to occupy" (uncertainty in position) and the "intensity of A’s movement" (uncertainty in velocity/momentum).

• If A is confined to a small space (restricting position):
  If A is forced into a cramped area—such as a tiny studio apartment or a restroom—stress and energy build up to a breaking point, leaving A restless and on the verge of an explosion.
  Consequently, the moment the door opens, it becomes entirely impossible to predict what A will do next—whether they will dash off to a neighboring prefecture or remain perfectly still. In other words, the uncertainty in their velocity becomes wildly unpredictable.

• If A is made to move at a steady, controlled pace (restricting velocity):
  Conversely, if A is instructed to walk at a constant, measured pace—say, 2 km/h—their mind enters a state of total detachment. A begins to wander aimlessly through a vast city.
  As a result, it becomes impossible for anyone to determine exactly where in the city A is located; the uncertainty in their position expands infinitely.

The relationship between A’s uncertainty in position ($\Delta x$Δx) and uncertainty in velocity/momentum ($\Delta p$Δp) can be expressed by the following equation: $\Delta x \times \Delta p \geq \dfrac{\hbar}{2}$Δx×Δp≥2ℏ​

Here, $\hbar$ℏ represents a constant—an inherent "degree of restlessness" unique to Person A—which can never be reduced below this value. (In standard physics, this constant is expressed as $\frac{h}{2\pi}$2πh​, where $h$h is Planck's constant.)

Main Problem

Person A wishes to lead the most stable life possible—one that is as efficient and balanced as it can be, both mentally and physically—by minimizing the sum of the fluctuations in their position and their velocity ($\Delta x + \Delta p$Δx+Δp).

Determine the values ​​of the "position fluctuation" ($\Delta x$Δx) and the "velocity fluctuation" ($\Delta p$Δp) that correspond to this most stable state.

Constraints

$\hbar=49357676.2568$ℏ=49357676.2568

Input Format

Provide the value of $(\Delta x+\Delta p)\times 100$(Δx+Δp)×100.