Particle in a box
In the particle-in-a-box model, the particle is confined between these types of walls.
infinitely high potential walls
This model approximates molecular vibrations.
harmonic oscillator
Rotational motion for a particle on a ring involves motion around this shape.
circle/ring
Quantum systems can only possess these allowed energy values.
quantized/discrete energy
Vibrational transitions are commonly observed using this type of spectroscopy.
infrared spectroscopy
The wavefunction for a particle in a box must equal this at the walls.
0
Unlike the particle in a box, the lowest energy of the harmonic oscillator is this value.
zero-point energy
Rotational energy depends on this molecular property.
moment of inertia
A standing wave forms only when this condition is satisfied.
constructive interference/boundary conditions
quantum harmonic oscillator
Energy levels in a particle in a box become more separated when the box becomes this.
smaller
The spacing between harmonic oscillator energy levels is this.
Rotational quantum numbers can be positive, negative, or this value
0
This explains why a particle cannot have zero energy in a box.
uncertainty principle
Absorption of energy causes transitions between these.
energy levels
This quantum number labels the allowed energy states in a 1D box.
n
Increasing the bond strength constant kkk causes vibrational frequency to do this.
increases
The angular momentum operator along the z-axis is represented by this symbol.
L^z
As quantum number increases, quantum behavior becomes more like this theory.
classical mechanics
The energy difference between quantum states determines this property of absorbed light.
frequency/wavelength
As the quantum number increases, the number of nodes changes in this way.
it increases
Lighter atoms vibrate at higher frequencies because frequency depends inversely on this quantity.
reduced mass
Rotational energy levels become closer together as the moment of inertia does this.
increases
Probability density is obtained from the wavefunction using this mathematical operation.
squaring the magnitude of the wavefunction
Spectroscopy works because molecules interact with electromagnetic radiation through these quantized motions.
vibrational and rotational motions