Quantum physics is physics that takes the postulate of the quantum as one of its foundations. It is mostly concerned with sub-atomic particles, atoms, and molecules, and the radiation that belongs to them.
The postulate of the quantum is that change in Nature is through jumps between sub-atomic stationary states.
There are three principal versions of quantum physics:
A fourth version, mainly the work of Louis de Broglie, is less widely studied.
Old quantum theory
The old quantum theory originated in 1900, with the work of Max Planck. It accepts the postulate of the quantum, but does not live by all of its consequences. A fundamental consequence of the postulate is that the finest possible observation is the detection of a single quantum. The old quantum theory does not recognize this, and consequently is unable to express itself in terms of strictly experimentally based concepts. For this reason, it is largely obsolete. Nevertheless, it has a degree of physical interest, for example in simple studies of the hydrogen atom, initiated by Niels Bohr.
Quantum mechanics replaced the old quantum theory, starting in 1925 and 1926, initiated by Werner Heisenberg and Erwin Schrödinger. Quantum mechanics fully lives by the postulate of the quantum. But it does not give a picture of quantal processes that is expressible in terms of ordinary physical space-time and its intrinsic partner, causality. This is because quantum mechanics is defined by a mathematical formalism that is built on the abstract concept of the wave function. The wave function has as its domain an abstract mathematical object called configuration space. Its range is another abstraction, the so-called "probability amplitude". Neither configuration space nor probability amplitude are intuitively visualizable or immediately recognizable in ordinary everyday language or thinking. In this they differ respectively from ordinary ideas of physical space-time and of betting odds. Consequently, there arise questions of interpretation of quantum mechanics.
A fundamental ontological category of quantum mechanics is the quantum state, represented in the wave function. An observed fact in quantum mechanics is primarily that the system of interest has shown itself to be in some quantum state. In general, a quantum state is not fully located in ordinary physical space-time.
Quantum field theory
Quantum field theory lives by the postulate of the quantum, but in a way that expresses experimental observations more directly physically than does quantum mechanics. Its primary observed facts are quantum detection rates as functions of ordinary physical space-time, rather than the somewhat abstract quantum states of quantum mechanics. This is expressed in the scattering matrix, rather than in the more abstract wave function that characterizes quantum mechanics. The domain of the field of quantum field theory is ordinary physical space-time, in contrast with the abstract configuration space of quantum mechanics. The range of the field of quantum field theory is still rather far from ordinary thinking; it is distinctly of a quantal nature. But the interpretational puzzles of quantum mechanics are eased in quantum field theory because the domain of the field is ordinary physical space-time. One way of expressing the profound difference between quantum field theory and quantum mechanics is in saying that quantum field theory is constructed by second quantization.
Ordinary physical space-time is a fundamental ontological category of quantum field theory, in contrast to quantum mechanics, which in some respects renounces it.
Albert Einstein was famously or infamously unhappy with quantum mechanics because its primary domain is configuration space, not ordinary physical space-time. Consequently, Einstein was deeply concerned that quantum mechanics has a serious problem with causality. Opposing Einstein in this, Niels Bohr preferred to renounce the claims of causality. In order to escape this problem of quantum mechanics, Einstein tried to develop a field theory along the lines of general relativity, including the sub-atomic processes studied in quantum physics. He did not succeed in this. But his concern is significantly addressed by quantum field theory. A possible fit between general relativity and quantum physics is a subject of active current research. In some respects quantum field theory is more physically complete than quantum mechanics, though merely mathematically, quantum mechanics may be regarded as complete. In physical interpretation, quantum field theory does not suffer from the causality problem of quantum mechanics.