# What is a bound state in quantum mechanics?

## 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”).