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Chapter 7: Problem 11

If a quantum particle is in a stationary state, does it mean that it does not move?

Short Answer

Expert verified
No, a quantum particle in a stationary state does not mean it does not move. The particle is in motion, but its motion and properties are unchanging over time.

Step by step solution

01

Understanding Quantum Particles

Realize that in quantum mechanics, the term 'particle' refers not to a tiny solid object, but rather to quantum systems with fixed energy levels. These systems can include things like atoms or electrons within atoms.
02

Comprehend Stationary States

Now understand what 'stationary' means. In quantum mechanics, a 'stationary state' is one in which the system's properties don’t change with time. Note that this doesn’t mean the system is not moving, it simply means its movement and properties are unchanging over time.
03

Applying to Quantum Particles

Apply the understanding from Steps 1 and 2. In a stationary state, a quantum system like electrons in a hydrogen atom, is not changing in properties over time. It may appear as if the electron isn't moving because it isn't changing states, but it in fact, it is in motion in a probabilistic sense defined by its wave function.

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Most popular questions from this chapter

A free proton has a wave function given by \(\Psi(x, t)=A e^{i\left(5.02 \times 10^{11} x-8.00 \times 10^{15} t\right)}\) The coefficient of \(x\) is inverse meters \(\left(\mathrm{m}^{-1}\right)\) and the coefficient on \(t\) is inverse seconds \(\left(\mathrm{s}^{-1}\right) .\) Find its momentum and energy.

A gas of helium atoms at \(273 \mathrm{K}\) is in a cubical container with \(25.0 \mathrm{cm}\) on a side. (a) What is the minimum uncertainty in momentum components of helium atoms? (b) What is the minimum uncertainty in velocity components? (c) Find the ratio of the uncertainties in (b) to the mean speed of an atom in each direction.

A 12.0 -eV electron encounters a barrier of height 15.0 eV. If the probability of the electron tunneling through the barrier is \(2.5 \%,\) find its width.

Show that \(\Psi(x, t)=A e^{i(k x-\omega t)}\) is a valid solution to Schrödinger's time-dependent equation.

Can a quantum particle 'escape' from an infinite potential well like that in a box? Why? Why not?
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