## What is a bound state in quantum mechanics?

In quantum physics, a bound state is a quantum state of a particle subject to a potential such that the particle has a tendency to remain localized in one or more regions of space.

### What is the quantum-mechanical ground state of a harmonic oscillator?

First, the ground state of a quantum oscillator is E0=ℏω/2, not zero. In the classical view, the lowest energy is zero. The nonexistence of a zero-energy state is common for all quantum-mechanical systems because of omnipresent fluctuations that are a consequence of the Heisenberg uncertainty principle.

#### What are bound and scattering states?

Mathematically, a bound state wavefunction rapidly decays as , even though the wavefunction can be non-zero in a classically forbidden region. Scattering state wavefunction is oscillatory even at infinity at least on one side (as or ).

Why bound states are discrete?

Bound states are the imginary energy states of a particle in a box or the stationary orbits of an atom of hydrogen or hydrogen like species. Each state is associated with a definite amount of energy and principal quantum number. These states are called discrete because there is no contact or overlap between two states.

Why quantum harmonic oscillator is quantized?

It takes on quantized values, because the number of atoms is finite. Note that the couplings between the position variables have been transformed away; if the Qs and Πs were hermitian (which they are not), the transformed Hamiltonian would describe N uncoupled harmonic oscillators.

## What is the quantum mechanical ground state energy of a harmonic oscillator Mcq?

The energy of the ground state of a 3d harmonic oscillator is zero.

### How many bound states are possible?

five bound states
There exist five bound states; their plots of |ψ|2 versus x are shown on the right side.

#### How many bound states are there in a finite potential well?

5 ”
The finite well has only 5 ”bound states.”

What is bound state wave function?

Bound state wave functions are standing waves. The eigenfunction is always exponentially decreasing for large |x|. The values of the eigen-energies can be approximated by fitting an integer number of half-wavelengths in the potential well. This approximation is best when V>>E in the edge regions (“infinite well”).