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In case you look at the checklist of the Forbes 40 richest folks in Singapore, you will notice many who made their fortunes growing and investing in real estate. Or simply look around you – the average Singaporean's wealth in all probability comes more from the appreciation of his HDB flat or non-public property than from another asset.
As my husband and I are also Singapore PR, we plan to take our criticism to our MP as properly, hopefully the government will turn into conscious of this drawback or perhaps they knew about it already, but it is time to take some action to right this lengthy standing grievance among patrons, and even amongst brokers who acquired shunned out from offers like my poor agent. She misplaced a sale for certain and unbeknownst to her, she in all probability never had an opportunity with that property proper from the start! I feel sorry for her, and appreciated her effort in alerting us about this unit and attempting to get us the property; but I'm a bit of aggravated or perhaps a bit resentful that we lost that condo basically as a result of we had been attached to her or any co-broke agent?
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In quantum mechanics, a stationary state is an eigenvector of the Hamiltonian, implying the probability density associated with the wavefunction is independent of time. This corresponds to a quantum state with a single definite energy (instead of a quantum superposition of different energies). It is also called energy eigenvector, energy eigenstate, energy eigenfunction, or energy eigenket. It is very similar to the concept of atomic orbital and molecular orbital in chemistry, with some slight differences explained below.
A stationary state is called stationary because the system remains in the same state as time elapses, in every observable way. For a single-particle Hamiltonian, this means that the particle has a constant probability distribution for its position, its velocity, its spin, etc. (This is true assuming the particle's environment is also static, i.e. the Hamiltonian is unchanging in time.) The wavefunction itself is not stationary: It continually changes its overall complex phase factor, so as to form a standing wave. The oscillation frequency of the standing wave, times Planck's constant, is the energy of the state according to the de Broglie relation.
- is a quantum state, which is a stationary state if it satisfies this equation;
- is the Hamiltonian operator;
- is a real number, and corresponds to the energy eigenvalue of the state .
Assuming that is time-independent (unchanging in time), this equation holds for any time t. Therefore this is a differential equation describing how varies in time. Its solution is:
Stationary state properties
As shown above, a stationary state is not mathematically constant:
However, all observable properties of the state are in fact constant. For example, if represents a simple one-dimensional single-particle wavefunction , the probability that the particle is at location x is:
which is independent of the time t.
As mentioned above, these equations assume that the Hamiltonian is time-independent. This means simply that stationary states are only stationary when the rest of the system is fixed and stationary as well. For example, a 1s electron in a hydrogen atom is in a stationary state, but if the hydrogen atom reacts with another atom, then the electron will of course be disturbed.
Spontaneous decay complicates the question of stationary states. For example, according to simple (nonrelativistic) quantum mechanics, the hydrogen atom has many stationary states: 1s, 2s, 2p, and so on, are all stationary states. But in reality, only the ground state 1s is truly "stationary": An electron in a higher energy level will spontaneously emit one or more photons to decay into the ground state. This seems to contradict the idea that stationary states should have unchanging properties.
The explanation is that the Hamiltonian used in nonrelativistic quantum mechanics is only an approximation to the Hamiltonian from quantum field theory. The higher-energy electron states (2s, 2p, 3s, etc.) are stationary states according to the approximate Hamiltonian, but not stationary according to the true Hamiltonian, because of vacuum fluctuations. On the other hand, the 1s state is truly a stationary state, according to both the approximate and the true Hamiltonian.
Comparison to "orbital" in chemistry
Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. An orbital is a stationary state (or approximation thereof) of a one-electron atom or molecule; more specifically, an atomic orbital for an electron in an atom, or a molecular orbital for an electron in a molecule.
For a molecule that contains only a single electron (e.g. atomic hydrogen or H2+), an orbital is exactly the same as a total stationary state of the molecule. However, for a many-electron molecule, an orbital is completely different from a total stationary state, which is a many-particle state requiring a more complicated description (such as a Slater determinant). In particular, in a many-electron molecule, an orbital is not the total stationary state of the molecule, but rather the stationary state of a single electron within the molecule. This concept of an orbital is only meaningful under the approximation that if we ignore the electron-electron repulsion terms in the Hamiltonian as a simplifying assumption, we can decompose the total eigenvector of a many-electron molecule into separate contributions from individual electron stationary states (orbitals), each of which are obtained under the one-electron approximation. (Luckily, chemists and physicists can often (but not always) use this "single-electron approximation.") In this sense, in a many-electron system, an orbital can be considered as the stationary state of an individual electron in the system.
In chemistry, calculation of molecular orbitals typically also assume the Born-Oppenheimer approximation.
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- Stationary states, Alan Holden, Oxford University Press, 1971, ISBN 19-851121-3
- Transition of state
- Quantum number
- Quantum mechanic vacuum or vacuum state
- Virtual particle
- Steady State
- Quantum Mechanics Demystified, D. McMahon, Mc Graw Hill (USA), 2006, ISBN(10) 0 07 145546 9
- Cohen-Tannoudji, Claude, Bernard Diu, and Franck Laloë. Quantum Mechanics: Volume One. Hermann, 1977. p. 32.
- Quanta: A handbook of concepts, P.W. Atkins, Oxford University Press, 1974, ISBN 0-19-855493-1
- Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles (2nd Edition), R. Eisberg, R. Resnick, John Wiley & Sons, 1985, ISBN 978-0-471-87373-0
- Physical chemistry, P.W. Atkins, Oxford University Press, 1978, ISBN 0-19-855148-7