Ground state

Tiny things have levels of power. Most things like to stay low. This low state is called the ground state. It is the calmest way to be. When things get more power, they jump up. This is called an excited state. A thing at its lowest power is at zero point energy. If a thing is very, very cold, it stays low. This is the ground state. It is like a quiet place to rest.

Everything in our world has levels of power. The lowest level is called the ground state. This is the calmest way for a system to be. It is also called a stationary state. At this level, the system has the least amount of power. This power is called zero-point energy.

If a thing gets more power, it moves to an excited state. An excited state is any level higher than the ground state. When things are at absolute zero temperature, they stay in the ground state.

In some cases, a system can have more than one ground state. We call this degeneracy. This means different ways to be in the lowest state. Some things, like a perfect crystal, have only one ground state.

In a tiny box, a particle has different wave functions. A wave function is a way to show where a particle is. For the ground state, the wave has no nodes. A node is a place where the wave is zero. This helps keep the power at its lowest level.

Everything in the universe has different levels of energy. The lowest possible energy level is called the ground state. In this state, a system is at its most calm and stable. Scientists also call this a stationary state. The energy at this very bottom level is known as zero-point energy. Any level higher than this is called an excited state. When a system gains energy, it jumps up to these higher levels.

How does a system stay in the ground state? One way to look at it is through temperature. The third law of thermodynamics tells us about this. It says a system at absolute zero temperature stays in its ground state. At this temperature, the system has the least amount of disorder, or entropy. Some things, like a perfect crystal lattice, have only one unique ground state. This means they have zero entropy at absolute zero. Other systems might have more than one ground state. This special situation is called degeneracy.

Scientists have studied how these states work using math. In one dimension, the ground state has a special rule. It cannot have any nodes. A node is a place where a wave function reaches zero. If a wave had a node, it would have more energy. You could lower the energy by smoothing out the wave. This would remove the node and create a lower energy state. Therefore, the true ground state must be smooth and have no nodes.

We can see these rules in real atoms and particles. For example, a particle in a tiny box has a ground state. Its wave function looks like a half-period sine wave. The energy for this particle depends on its mass and the box width. In a hydrogen atom, the electron has a ground state too. Its wave function is a shape centered on the nucleus. The electron is most likely to be at the Bohr radius. For hydrogen, the electron has an energy of -13.6 eV in this state.

These tiny energy levels even help us keep track of time. Since 1997, the definition of one second has been very specific. It is based on the caesium-133 atom. Scientists look at the transition between two hyperfine levels of its ground state. This happens at a temperature of 0 K. By measuring these tiny shifts, we can define time very accurately. It is amazing how the smallest states of matter guide our whole world.

In the world of quantum mechanics, every system has different levels of energy. The ground state is the most important level of all. It is defined as the stationary state of the lowest possible energy. This state is also known as the vacuum in quantum field theory. The specific energy found at this lowest level is called the zero-point energy. Understanding the ground state helps scientists understand how matter behaves at its most basic level. Any state with energy higher than this base level is called an excited state.

Systems move between these levels based on energy changes. When a system gains energy, it moves from the ground state to an excited state. Conversely, systems naturally seek the lowest energy state to remain stable. A key connection exists between energy and temperature. The third law of thermodynamics states that a system at absolute zero temperature exists in its ground state. At this extreme temperature, the system's entropy, or disorder, is determined by how many ground states are available.

Sometimes, a system can have more than one ground state. This phenomenon is called degeneracy. Degeneracy occurs when a unitary operator acts on a ground state and commutes with the system's Hamiltonian. If a system has many different ground states, it is said to have degenerate ground states. However, some systems are much simpler. A perfect crystal lattice is an example of a system with a unique ground state. Because it has only one ground state, it has zero entropy at absolute zero temperature.

Mathematics can prove specific rules about these states. In one dimension, the ground state of the Schrödinger equation has no nodes. A node is a point where a wave function reaches zero. Scientists use a proof by contradiction to show this. If a state had a node, its average kinetic energy could be lowered by removing that node. By deforming the wave function to remove the node, the energy decreases. Since the ground state must be the lowest energy state, it cannot have nodes.

This lack of nodes has important implications for how particles are positioned. Because the ground state has no nodes, it is spatially non-degenerate. This means there are no two stationary quantum states with the same energy and spin that differ only in position. However, ground states can still be degenerate if they have different spin states. For example, two states might have the same position-space wave function but different spins. This allows for a ground state to be degenerate without breaking the rule about nodes.

We can see these principles in specific scientific examples. Consider a particle trapped in a one-dimensional box. The wave function for its ground state is a half-period sine wave. This wave reaches zero at the two edges of the box. The energy of this particle is calculated using the mass, the Planck constant, and the width of the box. Another example is the hydrogen atom. The electron in a hydrogen atom has a ground state called the 1s atomic orbital. This is a spherically symmetric distribution centered on the nucleus. The electron is most likely to be found at a distance known as the Bohr radius. For hydrogen, the electron's energy in this state is -13.6 eV relative to the ionization threshold.

These tiny quantum states even allow us to measure time with incredible precision. Since 1997, the official definition of one second has been tied to the caesium-133 atom. Scientists measure the radiation from the transition between two hyperfine levels of the ground state. This measurement is taken while the caesium-133 atom is at rest at a temperature of 0 K. This connection between the smallest energy states and our measurement of time shows how fundamental the ground state is to our understanding of the universe.