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jasony
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Why must the ground state not have a node? And the first excited state must have 1 node.
jasony said:Why must the ground state not have a node? And the first excited state must have 1 node.
jasony said:Can we always write the wavefunction as [tex]\psi_n(x)=N_ng_n(x)\sum_i{c_{n,i}x^i}[/tex]?
Why?
Is there other simple proof for the nodeless property of ground state wavefunction?
jasony said:Can we always write the wavefunction as [tex]\psi_n(x)=N_ng_n(x)\sum_i{c_{n,i}x^i}[/tex]?
Why?
The ground state in quantum mechanics refers to the lowest energy state that a quantum mechanical system can have. It is the state in which a particle or system is at its most stable and has the lowest possible energy.
Excited states refer to any energy state above the ground state. These states have higher energy levels and are less stable than the ground state. When a system transitions from an excited state to the ground state, it releases energy in the form of radiation or heat.
In quantum mechanics, the ground state is determined by solving the Schrödinger equation for a given system. The solution yields the energy of the ground state and the corresponding wave function, which describes the probability of finding a particle in a certain position.
The ground state of a system can change if the system is subjected to external forces or interactions. For example, when an atom absorbs energy, it can transition from the ground state to an excited state. However, the ground state is always the lowest energy state that a system can attain.
The ground state is significant because it serves as a reference point for all other energy states in a system. It also determines the behavior and properties of a system, such as the spacing of energy levels and the stability of the system. Understanding the ground state is crucial for understanding the behavior of matter at a quantum level.