The _ground state_ of a [[Quantum Mechanics|quantum mechanical]] system is its [[Quantum State|state]] with the lowest possible [[Energy|energy]]. It is _stable_ because there is no state of even lower energy into which it could transition. Systems can have multiple [[Energy Level|energy levels]], or even an infinite number of higher-lying states, often referred to as _excited states_. An energy diagram of a typical system may look like this: ![[ground_state_diagram.excalidraw.light.svg]] In [[Quantum Many-Body System|quantum many-body physics]], which studies systems of many interacting quantum particles, determining the ground state is often a Herculean task. This [[Complexity Theory|complexity]] arises because quantum particles can be arranged in many possible ways, and identifying the correct configuration requires solving the [[Schrödinger Equation|Schrödinger equation]], which becomes intractable for large systems. However, understanding ground states is crucial because they dictate how physical systems behave at [[Absolute Zero Temperature|low temperature]], where quantum effects are most pronounced. A simple example of a ground state is found in the [[Bohr Model|Bohr model]] of [[Atom|atomic]] physics. When an electron occupies the lowest possible orbit, the atom is in its ground state. From here, the electron may absorb energy and transition to a higher-lying excited state: ![[ground_state_bohr.excalidraw.light.svg]] Traditionally, [[Classical Computer|classical computers]] have been used to determine ground states of physical systems. However, classical [[Algorithm|algorithms]] are only effective in special cases, such as when the [[Schrödinger Equation|Schrödinger equation]] can be solved efficiently. In most cases, solving for ground states is computationally very difficult. To overcome this limitation, researchers are now building [[Quantum Simulation|quantum simulators]] and [[Quantum Computer|quantum computers]] specifically designed for this task. Quantum systems can inherently simulate other quantum systems more efficiently than classical computers, making them powerful tools for exploring ground-state properties in quantum chemistry, materials science, and [[Condensed Matter Physics|condensed matter physics]]. >[!read]- Further Reading >- [[Hamiltonian Operator]] >- [[Energy Level]] >[!ref]- References