State the position-momentum uncertainty principle.

What is \(\hbar\) in terms of \(h\)?

Is the uncertainty principle mainly a statement about poor instruments?

An electron is localized to \(0.100\,\mathrm{nm}\). Estimate the minimum momentum uncertainty using \(\hbar=1.05\times10^{-34}\,\mathrm{J\,s}\).

A particle has \(\Delta x=1.0\times10^{-12}\,\mathrm{m}\). Estimate the minimum \(\Delta p\).

If \(\Delta x\) is made ten times smaller, what happens to the minimum possible \(\Delta p\)?

A particle has \(\Delta p=2.0\times10^{-24}\,\mathrm{kg\,m\,s^{-1}}\). Find the minimum \(\Delta x\).

State the energy-time uncertainty estimate.

A state lasts \(1.0\times10^{-9}\,\mathrm{s}\). Estimate the minimum energy uncertainty.

Convert \(5.25\times10^{-26}\,\mathrm{J}\) to eV using \(1\,\mathrm{eV}=1.60\times10^{-19}\,\mathrm{J}\).

Why does a narrow slit imply a spread in transverse momentum?

A beam is localized to a slit of width \(a\). What rough momentum spread scale follows from de Broglie reasoning?

Can \(\Delta x\) and \(\Delta p\) both be zero for the same particle state?

If \(\Delta x\) is very large, does the uncertainty principle force \(\Delta p\) to be large?

A particle is localized to nuclear scale, \(\Delta x=1.0\times10^{-15}\,\mathrm{m}\). Estimate \(\Delta p_{\min}\).

Why is confinement energy important for light particles such as electrons?

A short-lived excited state has lifetime \(2.0\times10^{-15}\,\mathrm{s}\). Estimate its minimum energy width in joules.

Convert the energy width in question 17 to eV.

Explain why the uncertainty principle is consistent with diffraction.

Derive the minimum momentum uncertainty for a given position uncertainty.