FIG 4 - uploaded by Helmut Linde
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The second excited state of the harmonic chain with wave number zero is similar to the first one shown in Fig. 3. But where the first excited state has only one 'nodal line' at q = 0 (or,
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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
... and the two-particle state Ψ = (a † 0 ) 2 Ψ 0 in Fig. 4. As before, the color scale is chosen such that configurations with Ψ = 0 blend in invisibly with the white background, and the lines in deepest red/blue correspond to the largest (positive) / smallest (negative) values of ...
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... case the polylines close to the q = 0 line tend to correspond to negative values of Ψ while those farther away from that line are rather associated with positive values of Ψ. This pattern obviously resembles the positive and negative parts of the energy eigenfunctions of a one-dimensional harmonic oscillator. The classical analog to Fig. 3 and Fig. 4 is a chain whose points masses oscillate synchronously and a stronger excitation of the chain as a whole corresponds to a higher number of particles in the quantum field. Fig. 3. But where the first excited state has only one 'nodal line' at q = 0 (or, much more precisely, one nodal hypersurface which contains the point q = 0), we can ...
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... and the two-particle state Ψ = (a † 0 ) 2 Ψ 0 in Fig. 4. As before, the color scale is chosen such that configurations with Ψ = 0 blend in invisibly with the white background, and the lines in deepest red/blue correspond to the largest (positive) / smallest (negative) values of ...
Context 4
... case the polylines close to the q = 0 line tend to correspond to negative values of Ψ while those farther away from that line are rather associated with positive values of Ψ. This pattern obviously resembles the positive and negative parts of the energy eigenfunctions of a one-dimensional harmonic oscillator. The classical analog to Fig. 3 and Fig. 4 is a chain whose points masses oscillate synchronously and a stronger excitation of the chain as a whole corresponds to a higher number of particles in the quantum field. Fig. 3. But where the first excited state has only one 'nodal line' at q = 0 (or, much more precisely, one nodal hypersurface which contains the point q = 0), we can ...
