Tunnelling Effect for Quadruples Potential Using Matrix Propagation Method

Semiconductor materials can be used as potential barriers to Tunnelling effects. In this study, four semiconductor materials are arranged in various ways to form a quadruple potential structure to analyze the value of the transmission coefficient. The analysis was conducted using the analytical and numerical matrix propagation method using Matlab2018a. The results confirmed that the inverted arrangement produces the same transmission coefficient value for each energy. So that there are 12 kinds of transmission coefficient values generated from 24 arrangements. The semiconductor material composition with the most considerable transmission coefficient value is ADCB and BCDA, which have a value of 0.8087. The variation of the arrangement affects the value of the transmission coefficient so that it can be used as a guideline for selecting the arrangement that produces the most optimum value of the transmission coefficient from various possible arrangements.

Origin of Probability in Quantum Mechanics and the Physical Interpretation of the Wave Function

The theoretical calculation of quantum mechanics has been accurately verified by experiments, but Copenhagen interpretation with probability is still controversial. To find the source of the probability, we revised the definition of the energy quantum and reconstructed the wave function of the physical particle. Here, we found that the energy quantum ê is 6.62606896 ×10-34J instead of hν as proposed by Planck. Additionally, the value of the quality quantum ô is 7.372496 × 10-51 kg. This discontinuity of energy leads to a periodic non-uniform spatial distribution of the particles that transmit energy. A quantum objective system (QOS) consists of many physical particles whose wave function is the superposition of the wave functions of all physical particles. The probability of quantum mechanics originates from the distribution rate of the particles in a state in the QOS per unit volume at time t and near position r. Based on the revision of the energy quantum assumption and the origin of the probability, we proposed new certainty and uncertainty relationships, explained the physical mechanism of wave-function collapse and the quantum tunnelling effect, derived the quantum theoretical expression of double-slit and single-slit experiments.

Origin of Probability in Quantum Mechanics and the Physical Interpretation of the Wave Function

The theoretical calculation of quantum mechanics has been accurately verified by experiments, but Copenhagen interpretation with probability is still controversial. To find the source of the probability, we revised the definition of the energy quantum and reconstructed the wave function of the physical particle. Here, we found that the energy quantum ê is 6.62606896 ×10-34J instead of hν as proposed by Planck. Additionally, the value of the quality quantum ô is 7.372496 × 10-51 kg. This discontinuity of energy leads to a periodic non-uniform spatial distribution of the particles that transmit energy. A quantum objective system (QOS) consists of many physical particles whose wave function is the superposition of the wave functions of all physical particles. The probability of quantum mechanics originates from the distribution rate of physical particles in a state in the QOS per unit volume at time t and near position r. Based on the revision of the energy quantum assumption and the origin of the probability, we proposed new certainty and uncertainty relationships, explained the physical mechanism of wave-function collapse and the quantum tunnelling effect, derived the quantum theoretical expression of double-slit and single-slit experiments.