Final answer:
The provided question is related to quantum mechanics, addressing the superposition of quantum states in qubits for quantum computing, the calculation of populations in quantum states, and the fundamental rules governing these states, like the Pauli Exclusion Principle.
Step-by-step explanation:
The question pertains to the realm of quantum mechanics, specifically the study of quantum states and qubits. Qubits are fundamental to quantum computing, as they hold data in mixed states of zero and one, unlike classic binary digits in traditional computing.
This allows quantum computers to potentially operate at much higher efficiencies for certain tasks. The superposition of qubits, as represented in the given quantum state, is crucial for the computational power of quantum computers.
In classical physics, two-state systems could refer to binary states such as on or off, while in quantum mechanics, similar systems (like electron spin, atom decay states, etc.) can exist in superpositions of these binary states. The concept is analogous to Schrödinger's cat being both dead and alive until observed.
This is a foundational concept in understanding the probabilistic nature of quantum mechanics and the calculation of populations of quantum states, such as in the problem asking for the relative populations of two quantum states with a given energy separation.
Quantum numbers and the Pauli Exclusion Principle are also integral to quantum mechanics, ensuring that no two electrons can occupy the same quantum state, which is characterized by a set of four quantum numbers. The principle is critical for the understanding of the electronic configuration and properties of elements.