Exact Solution of a Time-Dependent Quantum Harmonic Oscillator with Two Frequency Jumps via the Lewis–Riesenfeld Dynamical Invariant Method
Harmonic oscillators with multiple abrupt jumps in their frequencies have been investigated by several authors during the last decades. We investigate the dynamics of a quantum harmonic oscillator with initial frequency <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML&qu...
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| フォーマット: | 論文 |
| 言語: | English |
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MDPI AG
2022-12-01
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| シリーズ: | Entropy |
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| オンライン･アクセス: | https://www.mdpi.com/1099-4300/24/12/1851 |
| _version_ | 1827639820065701888 |
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| author | Stanley S. Coelho Lucas Queiroz Danilo T. Alves |
| author_facet | Stanley S. Coelho Lucas Queiroz Danilo T. Alves |
| author_sort | Stanley S. Coelho |
| collection | DOAJ |
| description | Harmonic oscillators with multiple abrupt jumps in their frequencies have been investigated by several authors during the last decades. We investigate the dynamics of a quantum harmonic oscillator with initial frequency <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>ω</mi><mn>0</mn></msub></semantics></math></inline-formula>, which undergoes a sudden jump to a frequency <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>ω</mi><mn>1</mn></msub></semantics></math></inline-formula> and, after a certain time interval, suddenly returns to its initial frequency. Using the Lewis–Riesenfeld method of dynamical invariants, we present expressions for the mean energy value, the mean number of excitations, and the transition probabilities, considering the initial state different from the fundamental. We show that the mean energy of the oscillator, after the jumps, is equal or greater than the one before the jumps, even when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ω</mi><mn>1</mn></msub><mo><</mo><msub><mi>ω</mi><mn>0</mn></msub></mrow></semantics></math></inline-formula>. We also show that, for particular values of the time interval between the jumps, the oscillator returns to the same initial state. |
| first_indexed | 2024-03-09T16:48:25Z |
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| id | doaj.art-f3bc9f5a430d45b6b0772a88722d9911 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-09T16:48:25Z |
| publishDate | 2022-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-f3bc9f5a430d45b6b0772a88722d99112023-11-24T14:44:11ZengMDPI AGEntropy1099-43002022-12-012412185110.3390/e24121851Exact Solution of a Time-Dependent Quantum Harmonic Oscillator with Two Frequency Jumps via the Lewis–Riesenfeld Dynamical Invariant MethodStanley S. Coelho0Lucas Queiroz1Danilo T. Alves2Faculdade de Física, Universidade Federal do Pará, Belém 66075-110, PA, BrazilFaculdade de Física, Universidade Federal do Pará, Belém 66075-110, PA, BrazilFaculdade de Física, Universidade Federal do Pará, Belém 66075-110, PA, BrazilHarmonic oscillators with multiple abrupt jumps in their frequencies have been investigated by several authors during the last decades. We investigate the dynamics of a quantum harmonic oscillator with initial frequency <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>ω</mi><mn>0</mn></msub></semantics></math></inline-formula>, which undergoes a sudden jump to a frequency <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>ω</mi><mn>1</mn></msub></semantics></math></inline-formula> and, after a certain time interval, suddenly returns to its initial frequency. Using the Lewis–Riesenfeld method of dynamical invariants, we present expressions for the mean energy value, the mean number of excitations, and the transition probabilities, considering the initial state different from the fundamental. We show that the mean energy of the oscillator, after the jumps, is equal or greater than the one before the jumps, even when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ω</mi><mn>1</mn></msub><mo><</mo><msub><mi>ω</mi><mn>0</mn></msub></mrow></semantics></math></inline-formula>. We also show that, for particular values of the time interval between the jumps, the oscillator returns to the same initial state.https://www.mdpi.com/1099-4300/24/12/1851Lewis–Riesenfeld methodquantum harmonic oscillatorabrupt jumps |
| spellingShingle | Stanley S. Coelho Lucas Queiroz Danilo T. Alves Exact Solution of a Time-Dependent Quantum Harmonic Oscillator with Two Frequency Jumps via the Lewis–Riesenfeld Dynamical Invariant Method Entropy Lewis–Riesenfeld method quantum harmonic oscillator abrupt jumps |
| title | Exact Solution of a Time-Dependent Quantum Harmonic Oscillator with Two Frequency Jumps via the Lewis–Riesenfeld Dynamical Invariant Method |
| title_full | Exact Solution of a Time-Dependent Quantum Harmonic Oscillator with Two Frequency Jumps via the Lewis–Riesenfeld Dynamical Invariant Method |
| title_fullStr | Exact Solution of a Time-Dependent Quantum Harmonic Oscillator with Two Frequency Jumps via the Lewis–Riesenfeld Dynamical Invariant Method |
| title_full_unstemmed | Exact Solution of a Time-Dependent Quantum Harmonic Oscillator with Two Frequency Jumps via the Lewis–Riesenfeld Dynamical Invariant Method |
| title_short | Exact Solution of a Time-Dependent Quantum Harmonic Oscillator with Two Frequency Jumps via the Lewis–Riesenfeld Dynamical Invariant Method |
| title_sort | exact solution of a time dependent quantum harmonic oscillator with two frequency jumps via the lewis riesenfeld dynamical invariant method |
| topic | Lewis–Riesenfeld method quantum harmonic oscillator abrupt jumps |
| url | https://www.mdpi.com/1099-4300/24/12/1851 |
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