FIG 5 - uploaded by Helmut Linde
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Quantum Field Theory (QFT) is the basis of some of the most fundamental theories in modern physics, but it is not an easy subject to learn. In the present article we intend to pave the way from quantum mechanics to QFT for students at early graduate or advanced undergraduate level. More specifically, we propose a new way of visualizing the wave fun...
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Context 1
... we turn to excitations of the chain with non-zero wave number. For example, the state Ψ = a † 1 Ψ 0 (which we can also write as Ψ {ν k } where ν k is equal to 1 for k = 1 and zero else) is represented in Fig. 5 for N = 15. Its classical analog is a standing wave in the oscillator chain. The location of the nodes near n = 6 and n = 13 can be explained by transforming back to the q n coordinates: In our state a † 1 Ψ 0 the oscillating system is excited along the˜Qthe˜ the˜Q 1 coordinate, since this is how we defined the creation operators in ...
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... graph of the state a † −1 Ψ 0 would look very similar to Fig. 5 with the exception that the standing wave is shifted by an offset of N/4 along the n-axis compared to the state a † 1 Ψ 0 . standing wave with two nodes in classical mechanics. It can be interpreted as one quantum particle in an energy eigenstate of the lowest non-zero kinetic ...
Context 3
... we turn to excitations of the chain with non-zero wave number. For example, the state Ψ = a † 1 Ψ 0 (which we can also write as Ψ {ν k } where ν k is equal to 1 for k = 1 and zero else) is represented in Fig. 5 for N = 15. Its classical analog is a standing wave in the oscillator chain. The location of the nodes near n = 6 and n = 13 can be explained by transforming back to the q n coordinates: In our state a † 1 Ψ 0 the oscillating system is excited along the˜Qthe˜ the˜Q 1 coordinate, since this is how we defined the creation operators in ...
Context 4
... graph of the state a † −1 Ψ 0 would look very similar to Fig. 5 with the exception that the standing wave is shifted by an offset of N/4 along the n-axis compared to the state a † 1 Ψ 0 . standing wave with two nodes in classical mechanics. It can be interpreted as one quantum particle in an energy eigenstate of the lowest non-zero kinetic ...
