- Forums
- Physics
- Quantum Physics
- Thread starter*Himanshu*
- Start date
- Tags
- Crystal latticeMeanQuantum mechaincsSchrödingerSchrodinger equationSemiconductors
In summary, the wavevector "k" in the Schrödinger equation represents the momentum of a particle in a quantum system. It is a vector quantity that describes the direction and magnitude of the particle's motion and is used to calculate the probability of finding the particle at a certain position in space. The value of "k" is determined by the energy of the particle and the properties of the system it is in.
- #1
*Himanshu*
- 1
- 0
why the solution for energy levels of electron in 1D crystal lattice as solved in Kronig penny model has used wave vector k differently then the Schrödinger equation solved for a free particle.
(only the conditions in the equation has changed not the maths...so the "USE" of wavevector 'k' must remain same and thus the physical significance)
Moreover I want to ask reason for below mentioned statements(source given at end)-
- >'We notice that exactly as in the case of the constant potential , the wave vector k has a twofold role: It is still a wave vector in the plane wave part of the solution, but also an index to yk(r) and uk(r) because it contains all the quantum numbers, which ennumerate the individual solutions.'
- >But in any case, the quantity k, while still being the wave vector of the plane wave that is part of the wave function (and which may be seen as the "backbone" of the Bloch functions), has lost its simple meaning: It can no longer be taken as a direct representation of the momentum p of the wave via p = [PLAIN]http://www.tf.uni-kiel.de/matwis/amat/semi_en/kap_2/illustr/h_quer.gif[I]k[/I][/B], or of its wavelength l = 2p/k, since:
Last edited by a moderator:
Physics news on Phys.org
- Understanding quantum states: New research shows importance of precise topography in solid neon qubits
- Time-compression in electron microscopy: Terahertz light controls and characterizes electrons in space and time
- New calculation approach allows more accurate predictions of how atoms ionize when impacted by high-energy electrons
- #2
- 17,874
- 1,661
Welcome to PF;
why the solution for energy levels of electron in 1D crystal lattice as solved in Kronig penny model has used wave vector k differently then the Schrödinger equation solved for a free particle.
... well those are different situations.
But how has the wave vector been used differently?
You can use any characteristic of a mode as a way to label (index) the mode.
- #3
tijana
- 16
- 1
For free particles. Wave function is flat wave given by wave number k: where k2=2mE/ћ2
- #4
Simon Bridge
Science Advisor
Homework Helper
- 17,874
- 1,661
Good point @tijana ... specifically, for free particles, the wave-vector can take on much any value, which makes it useless as a general index (although we can use the wave-vectors of two different waves as labels to distinguish them). In some constraining systems, though, the wave-vector must take on discrete values ... so it can be used as an index for the state rather than just the name of a wave.
Some character of a function being used as a label in no way changes how it is used in physics, the labels just help us have discussions.
Related to What does the wavevector "k" mean in the Schrödinger eq. ?
1. What is the wavevector "k" in the Schrödinger equation?
The wavevector "k" in the Schrödinger equation represents the momentum of a particle in a quantum system. It is a vector quantity that describes the direction and magnitude of the particle's momentum.
2. How is the wavevector "k" related to the energy of a particle?
The wavevector "k" is related to the energy of a particle through the de Broglie relation, which states that the wavelength of a particle is equal to Planck's constant divided by the particle's momentum (h/ k). This means that as the magnitude of "k" increases, the energy of the particle also increases.
3. What is the significance of "k" in the Schrödinger equation?
"k" is an important parameter in the Schrödinger equation because it helps describe the behavior and properties of particles in a quantum system. It is used to calculate the probability of finding a particle at a specific position and time in the system.
4. Does the value of "k" change for different types of particles?
Yes, the value of "k" can vary depending on the type of particle and the specific quantum system it is in. For example, the wavevector for an electron in an atom will be different from the wavevector for a photon in an electromagnetic field.
5. How is the wavevector "k" related to the wavefunction in the Schrödinger equation?
The wavevector "k" is related to the wavefunction through the wavefunction's spatial dependence. The wavefunction is a mathematical description of the probability amplitude of a particle in a quantum system, and "k" is used to describe the spatial variation of this probability amplitude.
Similar threads
IBloch functions and momentum of electrons in a lattice
- Atomic and Condensed Matter
- Replies
- 20
- Views
- 6K
Crystal momentum in a lattice.
- Atomic and Condensed Matter
- Replies
- 6
- Views
- 4K
IMean speed of electrons in a periodic potential / lattice
- Atomic and Condensed Matter
- Replies
- 3
- Views
- 2K
- Quantum Physics
- Replies
- 2
- Views
- 3K
IIs the Wavefunction Speed in Quantum Mechanics Wrong?
- Quantum Physics
- Replies
- 8
- Views
- 1K
What does k mean in E-k diagram?
- Atomic and Condensed Matter
- Replies
- 1
- Views
- 7K
How Does a GaAs Quantum Well Influence Electron and Hole Energies?
- Advanced Physics Homework Help
- Replies
- 1
- Views
- 2K
How Does the Brillouin Zone Influence Electron Wavefunctions in Solids?
- Atomic and Condensed Matter
- Replies
- 6
- Views
- 15K
In search for a holistic perspective on the physical reality
- Other Physics Topics
- Replies
- 2
- Views
- 7K
- Forums
- Physics
- Quantum Physics
