What is a transition in quantum mechanics?
1 Answer
In quantum mechanics, a **transition** refers to the process by which a quantum system (such as an atom, molecule, or particle) changes from one quantum state to another. Quantum states are defined by specific sets of quantized properties, such as energy, angular momentum, and spin. Transitions occur when these properties change due to interactions with external forces or fields, often accompanied by the absorption or emission of energy.
### Key Features of Quantum Transitions:
#### 1. **Initial and Final States**:
- Quantum systems exist in discrete energy states, often denoted by wavefunctions \(|\psi_i\rangle\) (initial state) and \(|\psi_f\rangle\) (final state).
- Transitions involve moving from one state (e.g., an excited state) to another (e.g., a lower-energy state, or the ground state).
#### 2. **Energy Conservation**:
- The energy difference between the initial and final states, \(\Delta E = E_f - E_i\), is either absorbed or released, typically as a photon (quantum of light) or phonon (quantum of vibration in solids).
#### 3. **Mechanisms of Transition**:
Transitions are typically induced by external influences such as:
- **Electromagnetic Radiation**: When an atom absorbs or emits a photon, causing an electron to transition between energy levels.
- **Collisions**: Interactions with other particles can transfer energy, inducing transitions.
- **Spontaneous Emission**: In this case, an atom or molecule naturally releases energy without external provocation.
#### 4. **Selection Rules**:
- Not all transitions are allowed. Selection rules, derived from the symmetry properties of quantum states and conservation laws (e.g., angular momentum), dictate whether a transition can occur. For example:
- In many cases, the change in angular momentum quantum number \(l\) must obey \(\Delta l = \pm 1\).
- Some transitions are "forbidden" but can still occur with lower probability (e.g., magnetic dipole or electric quadrupole transitions).
#### 5. **Types of Transitions**:
- **Electronic Transitions**: Involve changes in the energy of electrons in atoms or molecules. These are common in atomic spectra.
- **Vibrational Transitions**: Changes in the vibrational states of molecules, often occurring in the infrared spectrum.
- **Rotational Transitions**: Changes in the rotational states of molecules, usually observed in the microwave region.
- **Spin Transitions**: Changes in the spin state of particles, such as those involved in nuclear magnetic resonance (NMR).
---
### Examples of Quantum Transitions:
1. **In Atoms**:
- In the hydrogen atom, an electron transitioning from the \(n=2\) energy level to \(n=1\) emits a photon in the ultraviolet range, part of the Lyman series.
- Conversely, absorbing a photon can move the electron from a lower energy level to a higher one.
2. **In Molecules**:
- When a molecule absorbs infrared light, it may undergo a vibrational transition, changing its vibrational energy state.
3. **In Solids**:
- In semiconductors, transitions between the valence band and conduction band are responsible for the absorption and emission of light, fundamental to devices like LEDs and solar cells.
---
### Mathematical Description:
Transitions are governed by quantum mechanical probabilities calculated using the **time-dependent perturbation theory** and the **transition amplitude**:
- The **transition probability** is proportional to \(|\langle\psi_f | \hat{H}' | \psi_i\rangle|^2\), where \(\hat{H}'\) is the perturbing Hamiltonian (e.g., an electromagnetic field).
- If a photon is involved, its frequency \(\nu\) is related to the energy difference by Planck's relation: \(E_f - E_i = h\nu\), where \(h\) is Planck’s constant.
---
### Practical Significance:
Quantum transitions are the foundation of many physical phenomena and technologies, including:
- **Lasers**: Based on stimulated emission of light.
- **Spectroscopy**: Identifying elements and compounds via characteristic absorption or emission spectra.
- **Quantum Information**: Control of transitions in qubits forms the basis of quantum computing.
- **Astrophysics**: Spectral lines from atomic transitions are used to study stars and galaxies.
By understanding transitions, scientists can manipulate quantum systems, explore fundamental physics, and design new technologies.
### Key Features of Quantum Transitions:
#### 1. **Initial and Final States**:
- Quantum systems exist in discrete energy states, often denoted by wavefunctions \(|\psi_i\rangle\) (initial state) and \(|\psi_f\rangle\) (final state).
- Transitions involve moving from one state (e.g., an excited state) to another (e.g., a lower-energy state, or the ground state).
#### 2. **Energy Conservation**:
- The energy difference between the initial and final states, \(\Delta E = E_f - E_i\), is either absorbed or released, typically as a photon (quantum of light) or phonon (quantum of vibration in solids).
#### 3. **Mechanisms of Transition**:
Transitions are typically induced by external influences such as:
- **Electromagnetic Radiation**: When an atom absorbs or emits a photon, causing an electron to transition between energy levels.
- **Collisions**: Interactions with other particles can transfer energy, inducing transitions.
- **Spontaneous Emission**: In this case, an atom or molecule naturally releases energy without external provocation.
#### 4. **Selection Rules**:
- Not all transitions are allowed. Selection rules, derived from the symmetry properties of quantum states and conservation laws (e.g., angular momentum), dictate whether a transition can occur. For example:
- In many cases, the change in angular momentum quantum number \(l\) must obey \(\Delta l = \pm 1\).
- Some transitions are "forbidden" but can still occur with lower probability (e.g., magnetic dipole or electric quadrupole transitions).
#### 5. **Types of Transitions**:
- **Electronic Transitions**: Involve changes in the energy of electrons in atoms or molecules. These are common in atomic spectra.
- **Vibrational Transitions**: Changes in the vibrational states of molecules, often occurring in the infrared spectrum.
- **Rotational Transitions**: Changes in the rotational states of molecules, usually observed in the microwave region.
- **Spin Transitions**: Changes in the spin state of particles, such as those involved in nuclear magnetic resonance (NMR).
---
### Examples of Quantum Transitions:
1. **In Atoms**:
- In the hydrogen atom, an electron transitioning from the \(n=2\) energy level to \(n=1\) emits a photon in the ultraviolet range, part of the Lyman series.
- Conversely, absorbing a photon can move the electron from a lower energy level to a higher one.
2. **In Molecules**:
- When a molecule absorbs infrared light, it may undergo a vibrational transition, changing its vibrational energy state.
3. **In Solids**:
- In semiconductors, transitions between the valence band and conduction band are responsible for the absorption and emission of light, fundamental to devices like LEDs and solar cells.
---
### Mathematical Description:
Transitions are governed by quantum mechanical probabilities calculated using the **time-dependent perturbation theory** and the **transition amplitude**:
- The **transition probability** is proportional to \(|\langle\psi_f | \hat{H}' | \psi_i\rangle|^2\), where \(\hat{H}'\) is the perturbing Hamiltonian (e.g., an electromagnetic field).
- If a photon is involved, its frequency \(\nu\) is related to the energy difference by Planck's relation: \(E_f - E_i = h\nu\), where \(h\) is Planck’s constant.
---
### Practical Significance:
Quantum transitions are the foundation of many physical phenomena and technologies, including:
- **Lasers**: Based on stimulated emission of light.
- **Spectroscopy**: Identifying elements and compounds via characteristic absorption or emission spectra.
- **Quantum Information**: Control of transitions in qubits forms the basis of quantum computing.
- **Astrophysics**: Spectral lines from atomic transitions are used to study stars and galaxies.
By understanding transitions, scientists can manipulate quantum systems, explore fundamental physics, and design new technologies.