However, some decades ago there were also scientists, like the physicists Heisenberg and Schrödinger and the psychologist Piaget, who fulfill the criteria Brockman named for " third culture.

However, one needs at least 4 × 4 matrices to set up a system with the properties required — so the wave function had four components, not two, as in the Pauli theory, or one, as in the bare Schrödinger theory.

However, the Schrödinger equation predicts that there is a small probability that the ball will get to the other side of the hill, even if it has too little energy to reach the top.

However, since the Schrödinger equation is a wave equation, a single particle fired through a double-slit does show this same pattern ( figure on left ).

However, no-one, even Schrödinger and De Broglie, were clear on how to interpret it.

However, the concepts lead theoretical physicists, in particular Schrödinger, Dirac, Heisenberg and Feynman, to the development of quantum mechanics, and its refinement-quantum field theory.

However, many of Hartree's contemporaries did not understand the physical reasoning behind the Hartree method: it appeared to many people to contain empirical elements, and its connection to the solution of the many-body Schrödinger equation was unclear.

However, the necessity of reduction of Z by a number close to 1 for these K-alpha lines in heavier elements ( aluminum and above ) was derived completely empirically by Moseley, and was not discussed by his papers in theoretical terms, since the concept of atomic shells with paired electrons was not well established in 1913 ( this would not be proposed until about 1920 ), and in particular the Schrödinger atomic orbitals, including the 1s orbital with only 2 electrons, would not be formally introduced and completely understood, until 1926.

However, if the equation were based on the natural numbers for example, some of these operations ( like division and subtraction ) may not be valid as negative numbers and non-whole numbers are not allowed.

However, this equation becomes increasingly inaccurate at higher pressures and lower temperatures, and fails to predict condensation from a gas to a liquid.

However a more simple equation relating only the different energies in the fluid, known as Bernoulli's equation can be used.

However, globally human-made pollutants from combustion, construction, mining, agriculture and warfare are increasingly significant in the air pollution equation.

However, Bernoulli's equation states:

However, it is not yet clear what the full field equation will govern the dilaton in higher dimensions.

However, this equation may not be applicable to a comparator circuit which is non-linear and operates open-loop ( no negative feedback ).

However, when he explains in detail what he means, it is clear that he actually believes that his assertion is always true ; for instance, he shows that the equation x < sup > 4 </ sup > = 4x − 3, although incomplete, has four solutions ( counting multiplicities ): 1 ( twice ), − 1 + i √< span style =" text-decoration: overline "> 2 </ span >, and − 1 − i √< span style =" text-decoration: overline "> 2 </ span >.

However, the equation gives no information on the function's dependence on the variable y.

However, when we set corresponding coefficients equal in this case, the equation for x < sup > 3 </ sup > is

However in general, the equation is non-linear, and may lead to chaotic behaviour depending on how sensitive the system is to the initial conditions.

However, this equation only applies if the source resistance cannot be adjusted, e. g., with antennas ( see the first line in the proof stating " fixed source resistance ").

However, because is so much smaller than, the second term on the right in the above equation is small compared to the first, so doesn't have to be determined with high accuracy, and the balancing procedure described above is sufficient to give accurate results.

However, the equation of time can still be calculated for any time of the year, so an analemma can be graphed with this information.

However, the Council for Community and Economic Research ranked Fort Bend County as America's 3rd wealthiest county when the local cost of living was factored into the equation with median household income.

However, iconographically, such an equation is questionable, since what is considered the Classic Maya moon goddess, identifiable through her crescent, is always represented as a fertile young woman.

However, even in this simple example it may be observed that for ( arbitrarily ) small there are four other solutions to the equation ( with very large magnitude ).

However, there remains a further possible source of cancellation when computing and indeed this can lead to up to half of significant figures being lost: to correct for this requires to be computed in extended precision, of twice the precision of the final result ( see quadratic equation for details ).

) However, this was understood ( only ) in the language of equivalence classes of quadratic forms, so that in particular the analogy between quadratic forms and the Fermat equation seems not to have been perceived.

However, power consumption by a chip is given by the equation P = C × V < sup > 2 </ sup > × F, where P is power, C is the capacitance being switched per clock cycle ( proportional to the number of transistors whose inputs change ), V is voltage, and F is the processor frequency ( cycles per second ).

However, one does not need to know very much.

However, this does not mean that a child's teeth or jaws must necessarily resemble those of someone in his family.

However, she really does not know how to match the quantity of dollars given away by a quality of leadership that is basically needed.

However the Indo-European component of Apollo, does not explain his strong relation with omens, exorcisms, and with the oracular cult.

However, B's example of his uncle does not contradict A's statement, which says nothing about non-Republicans.

However, Rieux does not function as a first-person narrator.

However, it is important to remember that changing the order of operations does not involve or permit moving the operands around within the expression ; the sequence of operands is always unchanged.

However, for quasi-equilibrium systems ( e. g. spins out of equilibrium with the electromagnetic field ) this argument does not apply, and negative effective temperatures are attainable.

However, P does not remain constant during an adiabatic process but

However, it does seem clear that his first notable work, Summa Quoniam Homines, was completed somewhere between 1155 and 1165, with the most conclusive date being 1160, and likely was developed through his lectures at the school in Paris.

However, if we look for the peoples in the region from the upper Main in the north, south to the Danube and east to the Czech Republic where the Quadi and Marcomanni were located, Ptolemy does not give any tribes.

However, Amesbury in Wiltshire is in a different dialect region and does not easily fit into the pattern of the Midland dialect place names.

However, he does not immediately show what this principle might be.

However, it does contain several galaxies.

However, evidence indicates that harmala alkaloids act only on MAO-A, in a reversible way similar to moclobemide ( an antidepressant that does not require dietary restrictions ).

However, this does not apply to Emsam, the transdermal patch form of selegiline, which due to its bypassing of the stomach has a lesser propensity to induce such events.

However apoptosis induced by CDV in HeLa cells does not involve the initiator protein caspase-8.

However, for many acts the " off season " does not mean a period of inactivity, they use time for maintenance and practice.

However, passage of a bill by the state assembly alone does not change the law and the state senate and governor had not yet endorsed the bill.

However, Davy failed to develop a new theory, concluding that " acidity does not depend upon any particular elementary substance, but upon peculiar arrangement of various substances ".

However, DSM-IV-TR does not break amok down into two official categories.

However, in " A Great Day " Todd does thank the duo for giving him some gas money, and he allows them to watch him beat up someone who bumped into his car.

However, unlike Hollywood, Bollywood does not exist as a physical place.

However, this does not clarify who wrote the Aramaic portions of chapters 2-7.

However, this argument does not necessarily apply to bacteria.